diff --git a/src/client/src/tscFunctionImpl.c b/src/client/src/tscFunctionImpl.c
index 5a30d733fa4400b34092ebdb62c64a50b89da3d0..f4b244b18ad3ac065606dc359bf79420bef5fb32 100644
--- a/src/client/src/tscFunctionImpl.c
+++ b/src/client/src/tscFunctionImpl.c
@@ -15,19 +15,15 @@
 
 #include "os.h"
 #include "qAst.h"
-#include "qExtbuffer.h"
 #include "qFill.h"
 #include "qHistogram.h"
 #include "qPercentile.h"
-#include "qSyntaxtreefunction.h"
 #include "qTsbuf.h"
 #include "taosdef.h"
 #include "taosmsg.h"
 #include "tscLog.h"
 #include "tscSubquery.h"
-#include "tscompression.h"
 #include "tsqlfunction.h"
-#include "tutil.h"
 #include "ttype.h"
 
 #define GET_INPUT_CHAR(x) (((char *)((x)->aInputElemBuf)) + ((x)->startOffset) * ((x)->inputBytes))
@@ -920,6 +916,10 @@ static void minMax_function(SQLFunctionCtx *pCtx, char *pOutput, int32_t isMin,
   if (pCtx->preAggVals.isSet) {
     *notNullElems = pCtx->size - pCtx->preAggVals.statis.numOfNull;
     assert(*notNullElems >= 0);
+
+    if (*notNullElems == 0) {
+      return;
+    }
     
     void *  tval = NULL;
     int16_t index = 0;
diff --git a/src/query/src/qExecutor.c b/src/query/src/qExecutor.c
index d11933fb338405fd571b834f1e8652c0fc8cef68..2980332f7a3020113810a2412296be616815567e 100644
--- a/src/query/src/qExecutor.c
+++ b/src/query/src/qExecutor.c
@@ -4498,8 +4498,9 @@ static TSKEY doSkipIntervalProcess(SQueryRuntimeEnv* pRuntimeEnv, STimeWindow* w
 
     return key;
   } else {  // do nothing
-    pQuery->window.skey = tw.skey;
+    pQuery->window.skey      = tw.skey;
     pWindowResInfo->prevSKey = tw.skey;
+    pTableQueryInfo->lastKey = tw.skey;
 
     return tw.skey;
   }
@@ -4509,22 +4510,6 @@ static TSKEY doSkipIntervalProcess(SQueryRuntimeEnv* pRuntimeEnv, STimeWindow* w
 
 static bool skipTimeInterval(SQueryRuntimeEnv *pRuntimeEnv, TSKEY* start) {
   SQuery *pQuery = pRuntimeEnv->pQuery;
-
-  // get the first unclosed time window
-  bool assign = false;
-  for(int32_t i = 0; i < pRuntimeEnv->windowResInfo.size; ++i) {
-    if (pRuntimeEnv->windowResInfo.pResult[i]->closed) {
-      continue;
-    }
-
-    assign = true;
-    *start = pRuntimeEnv->windowResInfo.pResult[i]->win.skey;
-  }
-
-  if (!assign) {
-    *start = pQuery->current->lastKey;
-  }
-
   assert(*start <= pQuery->current->lastKey);
 
   // if queried with value filter, do NOT forward query start position
@@ -4540,6 +4525,7 @@ static bool skipTimeInterval(SQueryRuntimeEnv *pRuntimeEnv, TSKEY* start) {
   assert(pRuntimeEnv->windowResInfo.prevSKey == TSKEY_INITIAL_VAL);
 
   STimeWindow w = TSWINDOW_INITIALIZER;
+  bool ascQuery = QUERY_IS_ASC_QUERY(pQuery);
 
   SResultRowInfo *pWindowResInfo = &pRuntimeEnv->windowResInfo;
   STableQueryInfo *pTableQueryInfo = pQuery->current;
@@ -4564,19 +4550,25 @@ static bool skipTimeInterval(SQueryRuntimeEnv *pRuntimeEnv, TSKEY* start) {
     while (pQuery->limit.offset > 0) {
       STimeWindow tw = win;
 
-      if ((win.ekey <= blockInfo.window.ekey && QUERY_IS_ASC_QUERY(pQuery)) ||
-          (win.ekey >= blockInfo.window.skey && !QUERY_IS_ASC_QUERY(pQuery))) {
+      if ((win.ekey <= blockInfo.window.ekey && ascQuery) || (win.ekey >= blockInfo.window.skey && !ascQuery)) {
         pQuery->limit.offset -= 1;
         pWindowResInfo->prevSKey = win.skey;
+
+        // current time window is aligned with blockInfo.window.ekey
+        // restart it from next data block by set prevSKey to be TSKEY_INITIAL_VAL;
+        if ((win.ekey == blockInfo.window.ekey && ascQuery) || (win.ekey == blockInfo.window.skey && !ascQuery)) {
+          pWindowResInfo->prevSKey = TSKEY_INITIAL_VAL;
+        }
       }
 
-      // current window does not ended in current data block, try next data block
-      getNextTimeWindow(pQuery, &tw);
       if (pQuery->limit.offset == 0) {
         *start = doSkipIntervalProcess(pRuntimeEnv, &win, &blockInfo, pTableQueryInfo);
         return true;
       }
 
+      // current window does not ended in current data block, try next data block
+      getNextTimeWindow(pQuery, &tw);
+
       /*
        * If the next time window still starts from current data block,
        * load the primary timestamp column first, and then find the start position for the next queried time window.
@@ -4584,13 +4576,12 @@ static bool skipTimeInterval(SQueryRuntimeEnv *pRuntimeEnv, TSKEY* start) {
        * TODO: Optimize for this cases. All data blocks are not needed to be loaded, only if the first actually required
        * time window resides in current data block.
        */
-      if ((tw.skey <= blockInfo.window.ekey && QUERY_IS_ASC_QUERY(pQuery)) ||
-          (tw.ekey >= blockInfo.window.skey && !QUERY_IS_ASC_QUERY(pQuery))) {
-        SArray *         pDataBlock = tsdbRetrieveDataBlock(pRuntimeEnv->pQueryHandle, NULL);
+      if ((tw.skey <= blockInfo.window.ekey && ascQuery) || (tw.ekey >= blockInfo.window.skey && !ascQuery)) {
+
+        SArray *pDataBlock = tsdbRetrieveDataBlock(pRuntimeEnv->pQueryHandle, NULL);
         SColumnInfoData *pColInfoData = taosArrayGet(pDataBlock, 0);
 
-        if ((win.ekey > blockInfo.window.ekey && QUERY_IS_ASC_QUERY(pQuery)) ||
-            (win.ekey < blockInfo.window.skey && !QUERY_IS_ASC_QUERY(pQuery))) {
+        if ((win.ekey > blockInfo.window.ekey && ascQuery) || (win.ekey < blockInfo.window.skey && !ascQuery)) {
           pQuery->limit.offset -= 1;
         }
 
@@ -5767,7 +5758,7 @@ static void tableIntervalProcess(SQInfo *pQInfo, STableQueryInfo* pTableInfo) {
   SQuery *pQuery = pRuntimeEnv->pQuery;
   pQuery->current = pTableInfo;
 
-  TSKEY newStartKey = TSKEY_INITIAL_VAL;
+  TSKEY newStartKey = QUERY_IS_ASC_QUERY(pQuery)? INT64_MIN:INT64_MAX;
 
   // skip blocks without load the actual data block from file if no filter condition present
   if (!pRuntimeEnv->groupbyNormalCol) {
diff --git a/tests/script/general/parser/function.sim b/tests/script/general/parser/function.sim
index 3505ad1a28139a85e62193eddeb050dfde0bbc0d..110abc40c5c320f75a461cd366111505e3577d2a 100644
--- a/tests/script/general/parser/function.sim
+++ b/tests/script/general/parser/function.sim
@@ -244,3 +244,70 @@ if $data00 != -2.000000000 then
   print expect -2.000000000, actual: $data00
   return -1
 endi
+
+sql create table tm1 (ts timestamp,  k int);
+sql insert into tm1 values('2020-10-30 18:11:56.680', -1000);
+sql insert into tm1 values('2020-11-19 18:11:45.773', NULL);
+sql insert into tm1 values('2020-12-09 18:11:17.098', NULL);
+sql insert into tm1 values('2020-12-20 18:11:49.412', 1);
+sql insert into tm1 values('2020-12-23 18:11:50.412', 2);
+sql insert into tm1 values('2020-12-28 18:11:52.412', 3);
+
+print =====================> td-2610
+sql select twa(k)from tm1 where ts>='2020-11-19 18:11:45.773' and ts<='2020-12-9 18:11:17.098'
+if $rows != 0 then
+ return -1
+endi
+
+print =====================> td-2609
+sql select apercentile(k, 50) from tm1 where ts>='2020-10-30 18:11:56.680' and ts<='2020-12-09 18:11:17.098'
+if $rows != 1 then
+  return -1
+endi
+
+if $data00 != -1000.000000000 then
+  return -1
+endi
+
+system sh/exec.sh -n dnode1 -s stop -x SIGINT
+sleep 1000
+system sh/exec.sh -n dnode1 -s start
+print ================== server restart completed
+sql connect
+sleep 500
+
+sql use m_func_db0
+
+print =====================> td-2583
+sql select min(k) from tm1 where ts>='2020-11-19 18:11:45.773' and ts<='2020-12-20 18:11:49.412'
+if $rows != 1 then
+  return -1
+endi
+
+if $data00 != 1 then
+  print expect 1, actual: $data00
+  return -1
+endi
+
+print =====================> td-2601
+sql select count(*) from tm1 where ts<='2020-6-1 00:00:00' and ts>='2020-1-1 00:00:00' interval(1n) fill(NULL)
+if $rows != 0 then
+  return -1
+endi
+
+print =====================> td-2615
+sql select last(ts) from tm1 interval(17a) limit 776 offset 3
+if $rows != 3 then
+  return -1
+endi
+
+sql select last(ts) from tm1 interval(17a) limit 1000 offset 4
+if $rows != 2 then
+  return -1
+endi
+
+sql select last(ts) from tm1 interval(17a) order by ts desc limit 1000 offset 0
+if $rows != 6 then
+  return -1
+endi
+