you're looking for Google summer of code. I don't know if anybody else does it, but they do it. Unfortunately it is only in summers, but if you choose a project

you're looking for Google summer of code. I don't know if anybody else does it, but they do it. Unfortunately it is only in summers, but if you choose a project carefully you might be able to get external sponsorship throughout the year afterwards. Volunteer for open source projects that have funding you can potentially take advantage of