Where do I start regarding patenting a mechanism that underlies energy solution,considering I reside in Kenya and suffering from harsh economic conditions,currently my idea is in paper work as I cannot afford proving it
Practically,but works out in theory considering the necessary mathematical
Assumptions.

You can attempt to find a corporate sponsor (who very well may steal your idea) or you could contact a patent Attorney in Kenya.

I am positive you will need a prototype, not just an idea, in order to obtain a patent.

Uspto.gov has many resources for inventors. You can do a search by going to the search box at the top right side corner of the page and type something like: "foreign country patent filing" or use other related terms. Hope this helps. Good luck!