Video clipping problem.

The timeline indicator is always at the start of a frame. If you place the CTI at frame  14 and set an outpoint 14, you will get frame 14, but frame 14 will play until frame 15 starts, so the outpoint will be at the start of frame 15.

If you set an in-point at frame 14, the start point of the frame will be at frame 14. That is what is shown in your screenshot. There is nothing wrong. 

In an NLE like Premiere Pro, you get the same result if you set an in-point. The in-point will be at the start of the 14th frame, but if you set an out point or cut a shot at frame 14, you will not see any video because the shot will end at the start of frame 14. Those are industry-standard behaviors for 3D, animation, and compositing apps like After Effects, C4D, Blender, and video editing apps like Avid, Final Cut Pro, and Premiere Pro. 

I hope this helps. 

Without any info about your composition frame rates, the footage interpretation and so on nobody can tell you much. And as always: Cropped screenshots are useless. That said, I think you simply do not understand how AE handles time and frames and thus cannot get your timing in the way you want, but again, without some more info we can't know what you are actually doing. Fixing framerates would be a start, but otherwise you may need to use time-remapping to get fractional sub-frame placement. Anyway, start by reading the online help on these things:

https://helpx.adobe.com/after-effects/user-guide.html

Mylenium