“I enjoy frequently writing” or “I frequently enjoy writing” or “I enjoy writing frequently”?
It's not really a question of grammar, but a question of what you mean to communicate. I assume that what you mean is that you enjoy writing and that you frequently write. In your sentence it should be clear that "frequently" (or any adverb that you choose) refers to "writing" and not to "enjoy" or "enjoy writing". Compare the following:
"I enjoy frequently writing" — it may be interpreted as if what you enjoyed was to "write frequently".
"I enjoy writing frequently" — same as above.
"I frequently enjoy writing" — it may be interpreted as if you frequently enjoyed writing (but not always enjoyed writing).
Therefore, it's better if you split your sentence to avoid misinterpretation. I suggest something like:
Besides fishing, I also enjoy writing. I frequently write.
I hate to disagree with Bruno, but there is really nothing wrong with two of your examples:
Along with fishing, I enjoy writing frequently.
Along with fishing, I frequently enjoy writing.
The latter sounds more natural.
This is the kind of information one puts in the "Other Interests" section of one's résumé. What it represents is a kind of list, even though it contains but two items.
Items in a list don't have to be related by class: "I found four things in the box: a hammer, an old shirt, two books and a car battery." The only relationship between those items is that they were found in a box together. The only relationship between fishing and writing in your list is that they are things you enjoy doing. By stating your preference for fishing first, the reader assumes it is your primary interest. But the fact that you place it in a dependent clause indicates that you also hold writing in high esteem.
Furthermore, constructing the sentence in this way lets you imply that you do both things frequently without having to explicitly state that. And although to enjoy a pursuit means to like doing it, it is also a mild way of simply stating that you do something. If I say "I enjoy an occasional evening out with friends," that may mean I delight in the activity, or it may just mean that I "possess and benefit from" those evenings out. It is a way of saying that these evenings out are something I consider to be properly part of my domain.
In short, the ideas don't have to be split. And I must say I find Bruno's much-heralded suggestion,
Besides fishing, I also enjoy writing. I frequently write.
to be wordy, repetitious, unnecessary, and may not even mean what you originally intended. Certainly it has a different feel from the more relaxed "Along with fishing, I frequently enjoy writing." Perhaps I am wrong, and that is how you would prefer to say the idea after all. But don't be bullied just because a lot of people up-voted the answer.