It's no use "someone" / "someone's" doing something.

[sunsunmoon]

https://www.usingenglish.com/forum/ask-teacher/122290-its-no-use-us-telling.html
- It's no use someone doing something.
- It's no use someone's doing something.

Does either sound more formal than the other?

 

[5jj]

Discussions on this could go on for a long time. Some regard only the form with 's as correct; some regard it as the more formal of two correct forms; some say there is a difference in usage; and some feel that it is old-fashioned.

I tend to use 's myself, but the form without is more common.

The same would be true of me/my, you/your/etc