I am a British citizen, my father is Jamaican. Can i file papers for him to come to the UK?

Now that i am 18 i would like to see my father more. My mother is British, and until 3 years ago they were still together, but because of the difficulty of visa's and the price of flights, after 19 years and 2 children they split up. My sister and myself have just returned from Jamaica, where we spent a fabulous 3 weeks with my dad. He mentioned that now i am 18 i might be able to "file papers" for him to be able to come and visit, instead of him having to keep applying for a visitors visa, of which half the time is refused and then we have to go to London to plead to be able to see our dad. I am not sure what he meant or how to go about it and would appreciate any information that anyone may have. Regard Yasmin