Hello KA CHEUNG TSE,
Thank you for posting in Q&A forum.
If there are multiple DCs at the same site, the machines at the site will randomly find a domain controller at the site for authentication.
Based on the description, I understand you have site and DCs as below.
Site one
Old DC: Server 2012R2 (also DNS server)
New DC: Server 2016 (also DNS server, it is RWDC instead of RODC)
Site two
DC with FSMO roles (also DNS server)
other DCs
Maybe other sites with other Domain Controllers.
Please check:
1.Domain client machines set IP of the new DC (DNS server).
2.Please run DCdiag /v on new DC to check health of new DC.
3.Please check AD replication between all DCs. Run commands below on PDC to check.
repadmin /showrepl >C:\rep1.txt
repadmin /replsum >C:\rep2.txt
repadmin /showrepl * /csv >c:\repsum.csv
4.Please check AD ports.
Active Directory and Active Directory Domain Services Port Requirements https://docs.microsoft.com/en-us/previous-versions/windows/it-pro/windows-server-2008-R2-and-2008/dd772723(v=ws.10)?redirectedfrom=MSDN
Active Directory Replication over Firewalls
I hope the information above is helpful.
If you have any questions or concerns, please feel free to let us know.
Best Regards,
Daisy Zhou
============================================
If the Answer is helpful, please click "Accept Answer" and upvote it.