It all depends how the sentence continues. As we're not dealing with phrasal verbs here, the prepositions will be determined by the place or the thing which they refer to, not the verb which precedes them. If you're stuck 'somewhere', you should use whatever preposition is appropriate for the place in question. For example: stuck on an island stuck at school stuck in a traffic jam stuck under a bridge .... and so on. The same goes for places which are named e.g. stuck at Heathrow airport, stuck in Moscow, stuck on Mount Everest. The word 'stuck' isn't important in terms of the choice of preposition - what counts is that you are in, on or at a particular place. If you're using 'stuck' in a more figurative sense, we often use 'on'. For example, if you're doing an exercise with twenty questions and you can't do question 17, you might say "I'm stuck on Q17 ; if you're working through a textbook and you can't progress beyond chapter 5, you could say "I'm stuck on chapter 5".

Hi Alisa, you have to use the preposition 'in'

You are welcome. With words such as home and work, we normally use the preposition at. I'm stuck at home/at work.