Is it permissible for me to ask for some money as compensation for giving up the shop?.
If the rental contract was done, then it is binding on both parties and it is not permissible for one of them to annul it or cancel it except with the consent of the other party. Based on that, you are not obliged to cancel the contract and give up the shop to its owner; rather you have the right to oblige him to adhere to the contract between you.
And you can ask him for money, a small or large amount, in return for your giving up what remains for you of the rental period, and there is nothing wrong with that.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) said:
If this renter has a certain amount of time left, and the owner of the shop comes and asks him to leave before the end of that period, there is nothing wrong with him asking for compensation in return for giving up his right to the remaining time.
An example of that is if a person rented this shop for 10 years, then the owner of the shop comes after five years and asks him to vacate the shop for him. There is nothing wrong with the renter saying in that case: I will not leave and give up the remainder of the period except in return for such and such, because this is compensation for his right which is proven by the contract, which Allaah has enjoined us to fulfil, as He says (interpretation of the meaning): “O you who believe! Fulfil (your) obligations” [al-Maa’idah 5:1].
But if the rental period has ended, and the renter is staying in this shop on the basis of a state law, it is not permissible for him to refuse to leave except in return for compensation, meaning: it is not permissible for him to ask for compensation in return for leaving this shop when his rental period is up. Rather he must hand over the shop to its owner after the rental period has ended, and not take any compensation from him for that, because his staying in the shop without the owner's permission when the rental period has ended is wronging him, and wrongdoing is haraam, as Allaah says in the hadeeth qudsi: “O My slaves, I have forbidden oppression to Myself and I have made it forbidden among you, so do not wrong one another.” End quote from Fataawa Noor ‘ala al-Darb.
And Allaah knows best.