There's actually a few different facets of your question.
A) Working while on PTO during an emergency.
I've worked in jobs where, if you weren't able to handle an emergency situation (even during PTO), you wouldn't have a job there very long. Some places are like that, and you've indicated that you don't have a problem with that - that your problem is the non-production problems that they're disrupting your PTO over.
But this is why answers like "Don't answer your phone" or such don't work: you need to be available if there is an actual emergency situation.
B) Getting bothered by minor things during PTO by clients.
You didn't indicate this was a problem, but generally, something along the lines of, "Sorry, Bob Bobson, I'm on vacation until Tuesday next week. Since this isn't a critical production issue, it will have to either be handled by someone else or wait until I come back." Basically, polite (because you don't want to hack off the clients) but being firm in not doing any non-critical work while you're on vacation.
C) Getting bothered by minor things during PTO by an annoying coworker.
This is a similar situation to B, except it's a lot less forgivable coming from a coworker. They know you're out on vacation. They know what they're doing is rude and that what you're being contacted over isn't critical. The first time, treat it like it's B, but if they persist and keep calling? "Bob, you need to stop contacting me while I'm on vacation for non-critical issues. Do not call me again unless there's a critical production issue - this is my vacation, understand?"
TL/DR; Essentially, you need to keep the line of communication available while insisting that only a few things should ever be going through that line.
EDIT: Regarding the schism that seems to be appearing in answers/comments about "Should you be accessible for work during PTO?"
I worked a few years in an IT role within Manufacturing. Which places IT in a very central spot in terms of revenue: if critical programs/computers/etc go down, it's directly costing the company about $10,000... per hour.
At that point, it's not an issue of bus factor. We were expected to be able to fix and troubleshoot problems from any programs and have at least a minimal knowledge of what all the programs/databases/etc did. But if it'll take me 2 hours to solve a critical downtime and my coworker can solve it in 15 minutes? Well, the company has $17,500 at stake in my coworker doing it if possible. If it's not critical? Then the 2 hours is fine.
This by itself isn't nefarious. When I was interviewing for this job, they indicated that this was a high-availability role - that if there was a critical uptime issue, we were expected to be on-call regardless of vacation or holiday. Which is why they were paying about 5% more than other roles, as well as offering an average 18% yearly contingent salary bonus. I accepted this, and had no problems with this (the company had all sorts of other problems, but expected availability was communicated up-front and was suitably compensated, in my opinion.)
Just something to keep in mind - not all IT roles are the same. Not all have the same expectations or requirements for availability. As long as those expectations/requirements are transparent and up-front - and are happily agreed to by all parties - then there's not really an issue. And with that in mind: the OP isn't asking about critical production bugs while on vacation - they've said that they're fine with that. It's the non-critical stuff that a coworker is bothering them about.
Second Edit: Dear lord people! This keeps getting comments about "Kevin got screwed over by the company" or "Oh, the company should handle it like this" or "They should do a reward scheme like this". Two huge, major points:
- My company Did reward me. They wrote me a freaking check for
~$13,000 dollars as a yearly bonus - and that's the after tax
amount. I knew going in to the job I'd be doing off-hours support
or even potentially during PTO/holidy. It didn't happen often, but
when it did, I certainly felt well compensated for my time! Arguing
about different financial compensation schemes is way off point.
- The OP's question isn't even about production support during
PTO/holidays. It's about non-critical stuff. The OP has said
that they're fine with the occasional interruption to fix a
critical issue. The thing that's bugging them is the obnoxious
coworker that's pestering them with trivial stuff. That's their question.
In short: everyone seems to be assuming that the OP is getting crushed, burned-out, and destroyed by critical production issues while they're on vacation. That's not what they're saying, and there's no indication that there's a problem on that front. OP's question is about trivial stuff - that's the question they're looking for an answer on.