Postgressql - could not fork new process for connection: Cannot allocate memory Postgres instance restarted multiple times with out of memory errors. could not able to get what process would have consumed all memory.
2020-09-03 04:54:14 PDT LOG:  could not fork new process for connection: Cannot allocate memory
TopMemoryContext: 799496 total in 13 blocks; 63080 free (17 chunks); 736416 used
  TopTransactionContext: 8192 total in 1 blocks; 7960 free (0 chunks); 232 used
Here are the current settings. Postgres version is 10.5.12

effective_cache_size                | 16GB  
maintenance_work_mem                | 1GB     
max_wal_size                        | 4GB                                                                                      
max_worker_processes                | 8       
temp_buffers                        | 8GB                    
work_mem                            | 256MB 
shared_buffers                      | 32GB 
max_connections                     | 3000  


vm.overcommit_memory = 2
vm.overcommit_ratio = 80

-sh-4.2$ free -g
              total        used        free      shared  buff/cache   available
Mem:             62           9           0          36          52          16
Swap:             0           0           0   

Can you please suggest if any configuration changes required.
If each of these 3000 connections used work_mem only once (this limit is per node of the query plan, so it can be used several times by one database session), that could use almost 1TB RAM. I am not surprised that you are going OOM.
max_connections = 3000 is an insane setting. Do you have 3000 cores? Can your storage subsystem handle 3000 concurrent I/O requests?
I recommend that you use pgBouncer or another connection pool to reduce the number of database sessions.
By the way vm.overcommit_ratio should be 100 if you have no swap, otherwise you cannot allocate more than 80% of the available RAM (but perhaps that's on purpose).