The phrase "middle of a sentence" refers to the point in time when one is speaking or writing, but has not yet finished expressing their complete thought. Full definition
If you have an idea while the other person is talking, don't wait for him or her to finish: bust right in and interrupt in the middle of a sentence.» (inc.com)
There are two places in spontaneous speech where filler words commonly appear, Cohen explains: at the beginning (e.g. um, uh, so) and in the middle of a sentence (e.g. like, you know what I mean). (qz.com)
Of the two, filler words located in the middle of a sentence — also known as discourse markers — are not as noticeable, and are not as readily perceived as a filler word, than those in the front and tail end of a thought. (qz.com)