I feel bad if I say no. This sounds like a "you" problem that you need to make a "them" problem.

@JoelEtherton, would you just say "no"?

From option 2 it sounds like part of the goal of these meetings is to assign work so everyone knows who is doing what. Do I have that right?

@BSMP, 2 was during the sprint planning I think. There was a task that needed to be done. It was more related to my colleague's role on the project, but could also be seen as in between of our areas of responsibility.

@sf02. Nothing :) Just listening.

When you say, "...if I mention it was actually me, I will be seen as not a team-player." Is it Peter saying that or management? Is that something you've been told before in this job?

"No" is a complete sentence.

"I'm not sure how to deal with it" and in the next sentence "I have some ideas, will be able to do that on my own" would make me immediately say "now what, can you or not?".

Do you have a Daily meeting where you report on your progress? If you put in more than an hour of effort into helping with issue that is not your current task, I would mention that on the next day: "[your own report]... and I helped Peter with XY, that also took a bit of time." Then everybody knows, nobody should be offended, but if Peter is annoyed by you reporting your input, well, you might not have to worry about him asking anymore. ;)

Is work assigned officially? (During those meetings or otherwise.) In which case: "Sure I'll help, but run it past $BOSS first as I've got other issues on my plate and your issue would probably take $M hours at least. I will need to re-prioritise." Make sure to get the go-ahead from $BOSS (or official system) and not from $PETER. So $PETER now needs to make it known you are involved.

@HawkingRadiation Your comment is the best answer IMHO; why not make it an answer?

@bob Thank you. I didn't want to post it immediately because I do not know if the OP has Daily meetings, and it hinges on that assumption. Nonetheless, I have added it as an answer now.

As @fr13d says, boss will probably need to know what OP is spending their time on anyway so go mention it to Boss before doing any of the work. "After the meeting Peter decided it might help if I ..... Is that okay with my schedule?" You are being a team player but Boss at least knows you worked on it.

Do you use a ticketing system like JIRA? If not, recommend it; it solves this problem immediately since you can simply say 'sure, assign the ticket to me' and then management will see who actually resolved it.

Do you do regular/daily standups where you discuss what you did, what you're doing, and what you're stuck on? If so, it would be the perfect opportunity to mention that you helped "Peter" figure out something he was having trouble with.

"if I mention it was actually me, I will be seen as not a team player." - no, you will be seen as not a doormat, someone whose time is valuable.

I'm not really thrilled with all the JIRA suggestions, who resolves the ticket isn't meant to mean "this person did the work", if you start putting more weight into the meaning of that JIRA might be yet another thing to be gamed (plus who "wins" in collaborative projects?). "Peter" isn't dumb, they will figure out what's going on immediately and will just find a new system to game. Though personally, I think tickets are a pretty bad way to measure day to day dev work anyway.