Patching a cracked concrete/brick walkway
Looking at your pic, I think you have a couple of problems to solve. the reason the bricks broke in the first place is that the base under the edge of the bricks is too low or uneven. This cause the edge of the bricks to break under pressure. I also see that the crack has traveled further to the inside brick and that one as well as the mortar joint is cracked.

I think you really need to remove the broken bricks, clean off the mortar best you can, then fix the base and replace the bricks and mortar. Simply use a cold chisel, and hammer to remove the broken bricks and mortar.  Lay in some fine base, (stone dust, or similar), compact it well with a block and mallet. Moistening the base material helps a bit here. Dry fit the bricks to check the base height, then butter the replacement bricks, place them and point the joints.

I would also be checking the other edge bricks to assure there are no voids under the edge, or the same thing will happen to other bricks. If there are voids, try packing fill under them and along the outside border. The edges of these bricks need to be on a solid base or you will continue to have broken edges and cracked mortar.