I've been making music for 4 years now and I'm interested in making music for a game, and I want to get paid for it but can't find any opportunities for my skill.

To be honest, I think there are a lot of ways to find a gig or even bigger projects. Most of the bigger ones I think it usually come by the same way as film sountrrack: networking. That means, it's good to invest on connecting professionally with people around the globe and the right opportunity will come.

well, is very rare to find someone that needs music for their games in itch.io (you usually find people who wants to put their music in games actually), so if you want to get paid with music, your best option is to level up and start making music for more stuff other than games only... consider freelancing. There are sites like fiverr where you can be paid to make something for someone, and sites like soundbetter, which are more intended for music. Also, consider stock music sites like audiojungle, people pay to be able to use a song in everything they need (more passive money, what usually means a chiller income source in exchange of less money)