Can you tell us what you are doing, so we can tell you what else to try?
At full zoom, use the right and left arrow keys instead of playback. That will move the CTI one frame at a time.
You can't get more precise than that!
Probably the easiest way to do what I think you are asking for is to Dbl-click the full Clip in the Project Panel. This will open it into the Source Monitor. There, you can set the In & Out Points to the frame level. Then, drag that "instance" of the Clip to the Timeline. Reset the In & Out Points, as needed, and repeat by dragging THAT instance to the Timeline. You can do this as many times, as you need. Though you are working from the same "Source Clip," each instance on the Timeline will be basically a "Sub-Clip." Note: in PrPro, there are Sub-Clips, but they are a bit different, in a few aspects.
As Steve points out, one cannot edit Video to less than the frame-level. Even if one changes the TimeCode to Audio Units, the Video cannot be less than one frame, i.e. 1/30 sec. with NTSC and 1/25 sec. in PAL.
Good luck, and if I missed what you want, please step me through where I went wrong,
I need to catch .5 second to 2 second clips from usually the news or chat shows around the news
With NTSC, this means that you need from 15 frames to 60 frames, and with PAL footage, 12 frames and 50 frames. That will be easy to do in the Source Monitor, as I describe above.