Looking on the internet deeply has found these results:

stay in my side is the most popular phrase on the web.

stay on my side 1322,000 results on the web	stay in my side 13,510,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Phil can stay on his side, I'll stay on my side. Now he wants to stay on my good side. Yes. The casino works hard to stay on my good side so I don't make trouble for the folks who zoom in and out of there all weekend. Look, I completely understand and I promise I'll stay on my side of the bed. Phil can stay on his side, I'll stay on my side. You know, I'll stay on my side of the bed. So long as you stay on my side I'll be satisfied Considering that you will never be leaving this country again I would say it is in your best interests to stay on my good side.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

stay on my side

1322,000 results on the web

stay in my side

13,510,000 results on the web

More popular!

Phil can stay on his side, I'll stay on my side.
Now he wants to stay on my good side.
Yes. The casino works hard to stay on my good side so I don't make trouble for the folks who zoom in and out of there all weekend.
Look, I completely understand and I promise I'll stay on my side of the bed.
Phil can stay on his side, I'll stay on my side.
You know, I'll stay on my side of the bed.
So long as you stay on my side I'll be satisfied
Considering that you will never be leaving this country again I would say it is in your best interests to stay on my good side.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.