Concrete – How to fill gap between garage floor and driveway

You have divots in a concrete driveway.

I'd saw around the divot area, break it all out, and pour concrete, rather than anything to do with asphalt. Drill some holes in the edges and insert steel to tie the patch to the slab.

If following the "quick fix" fill-on-top approach, possibly thinset (tile cement) but trying to do anything with concrete in the winter is fraught with difficulty - you have to heat it up and keep it warm - if it freezes before it cures, it's toast.

My gut says that your quick fix with hot tar is going to be good for 6 months, at most. Additionally, it will complicate doing a good concrete repair later.

Since there will be now way to insure the concrete will be the same color or will it be able to tie in the texture to make the new pour "go away", neatly slope the concrete up towards the post say about a 1/2" to create a break line where the new concrete meets the old. Try to keep the slope uniform from post to post just so it will look professional. The slope will help drainage, even though the concrete acts like a huge sponge, holding moisture to the post, but it is much better than soil.

New concrete can smear over the old making a mess, but after a few hours, you can carefully clean the old concrete with a DAMP stiff bristle brush, no flowing water, taking MUCH care to not let the brush touch the fresh concrete. You may even wait 6 hrs and still accomplish this task.