Actually, I'd like to know if is correct to say: "I am trying fixing this", or should use the more obvious "I am trying to fix this"?
If the first one is correct, is there a name for this kind of syntax/conjugation?
If the verb to try is being used in the sense of to attempt, then it is generally followed by to + infinitive rather the -ing form of the verb. So, assuming that the trying here is attempting, it should be:
If, on the other hand, the verb is being used in the sense of testing something out (e.g. to see if it works or if you like it), then it is usual to follow it with the gerund:
However, the difference between the two senses of try is not always so clear-cut. A popular song from poor Alicia Keys has the lines:
Have you ever tried sleeping with a broken heart?
where the first try seems to mean attempt and the second means test out.
[And Irene is right that consecutive -ing forms can sound a little awkward.]
Although it is possible to have an -ing form after the verb try, two consecutive -ing forms sound very unnatural, so you'd better avoid it.