Seeing it on your PC
Some legitimate software does use 4444, so the port alone proves nothing. A connection on 4444 between your PC and an internet address you do not recognise deserves a close look.
Should you block it?
Find the program first. If you cannot explain it, disconnect from the network and scan the PC.
Check it on your PC
Run this in PowerShell to see what is using port 4444 right now, and which program owns it:
Get-NetTCPConnection -LocalPort 4444 -ErrorAction SilentlyContinue | Select-Object LocalAddress,LocalPort,RemoteAddress,RemotePort,State,@{n='Process';e={(Get-Process -Id $_.OwningProcess -ErrorAction SilentlyContinue).ProcessName}}No output means nothing is using the port at the moment. For every connection at once, paste netstat -ano into the netstat explainer.
Block it in Windows Firewall
In PowerShell run as administrator, this stops other computers from connecting to this port on your PC. It does not stop your own programs connecting out.
New-NetFirewallRule -DisplayName "Block inbound TCP 4444" -Direction Inbound -Protocol TCP -LocalPort 4444 -Action Block
Undo it with Remove-NetFirewallRule -DisplayName "Block inbound …", using the same name. If you depend on the service on your local network, this rule stops that too.