Water is sometimes able to penetrate the concrete because of damage to the surface or just deterioration over time.
Repair cracked concrete window sill.
Other option measure it all up make up a timber mould and cast a new one fix either a piece of half round dowel or sash cord to create the drip cast the cill upside down this method will be better than trying to cast in situ plus no weak joints.
If the sill is painted repaint the whole sill as this will give an overall better finish.
Brush the sill with a soft brush to remove dust and dirt before applying the first coat of masonry paint after any of the following work has been done if required of course.
What would be an appropriate material to fill it with.
Dust from the sill will rub into the filler making it dirty but also blending it in with the rest of the sill.
Use mortar mix on the block and replace the pieces.
If the sill is plain concrete it will not need to be painted.
Fix any small or medium cracks in your concrete window sill with caulk.
I have on hand a tube of big stretch caulk and a tub of dap bondex ready mixed concrete patch.
Steel reinforcing bars are cast into the center of the sill to strengthen it.
Concrete has high compression strength but low resistance to bending tensile strength so the steel reinforcement is necessary.
Finishing the mortar joint.
Scrape away any mess with the edge of the knife.
Any cracks can be sealed with the mortar mix or cement based caulk.
Allow to dry completely before applying a second and third coat.
Remove the excess material build up on the putty knife.
Fit the narrow tip of a bottle of silicone latex caulk into each crack and overfill it by about inch.
I have an exterior concrete window sill that has a crack in it that i want to patch pic attached.
However you should be able to purchase grey exterior filler which will be a close match to the concrete.
If you have the pieces just clean off any loose mortar from the block.
Sand down the filler when it is completely dry.
Using a small putty knife starting at the window smooth the caulking flush to the sill.