I'm not that good in music theory. There is this rhythm I can't find the right way to notate. Logic Pro shows it like this: (if you need mp3. let me know).
I don't personally see anything wrong with this notation; it's perfectly clear! If I came across it in a score, I would know exactly what was intended.
It's a slightly tricky rhythm to perform, because the performer must subdivide the first two sixteenth notes in three before immediately switching to a duple subdivision starting on the third sixteenth note. But this is a standard skill, so most competent musicians will perform it without problem.
This rhythm looks 100% correct to me as is, and I don't see any reason to try to improve it. But one possible improvement, as Heather S. mentions in the comments, is to beam all of the right-hand sixteenth notes into one beat:
If you're worried by what appears to be five sixteenth notes in the span of only four, the first three are part of a triplet. See What exactly does a 3 mean over a quarter note and an 8th note?
I don't see any mistakes in the notation, although the alternative beaming suggested by Heather S. and Richard is a good idea for clarity.
However, looking at the piano roll screenshot that you posted, and speaking from experience, perhaps that is not exactly what you intended to write. Automatic notation tends to cluster some of the notes and also create unwanted offbeats. What I see on the piano roll looks more like this to me: