A more general answer is that there are usually many ways of saying something. There may be large or subtle differences in meaning. "Would you stop talking about nothing by Jerry"; "would you stop talking just about Jerry"; "enough already about Jerry!"; "Jerry, Jerry... would you stop beating a dead horse?"; "Hey, it's time to change the subject, I'm sick of hearing about Jerry"; etc.

No, the first option does not work. "besides" in this instance means "anyone other than" Jerry. "About" is a preposition that means "referring to" Jerry. They are used very differently.

Is There Two Options To Say The Same Thing Or Not? / Incorrect Is there another way to say this sentence?, Is there a second way to say this sentence? / Correct I hear a lot of Russian speakers say "Besides", Beside means "next to" most of the times. F.e, Tom is sitting beside Jerry. As for your question, if there's an alternative to"Stop talking about Jerry only" you can say "Let's talk about something else" or "Switch the topic".

You may also say: Do not say anything about Jerry, please.

ARE there two options