MsEdge.exe is a genuine process, it is safe and there is no need to worry if you see it running. But maybe it's not. A virus or malware can masquerade as a genuine process. To know whether the process running on your system is genuine or not, we need to check the location.
To do that, open Task Manager, go to the Details tab, look for msedge.exe, right-click on it, and select Open File Location. You will be redirected to a location in File Explorer, where you will see the msedge.exe process. Your location should be the following.
C:Program Files (x86)MicrosoftEdgeApplication
If you are still suspicious, you can right-click on msedge.exe from File Explorer and then select Scan with Defender. This will scan the file and give you the result.
In case, scanning yields no result and you for some very obvious are suspecting that there are some viruses on your system, you can try using your antivirus to scan the system. If you don't have an antivirus, then follow the given steps to use Windows Defender to scan your system on Windows 11/10.
Search out "Windows Security" from the Start Menu.
Go to Virus & threat protection > Scan options.
Select Microsoft Defender Offline scan and click Scan now.
Let it run, and hopefully, it will resolve the issue for you.