If you would make the custom mob you want to get points from killing, drop a specific item then you could execute off the item. Here is a example... Summon in the custom mob use a command like this:

/summon Zombie ~ ~1 ~ {CustomName:"Custom Zombie",CustomNameVisible:1,Equipment:[{},{},{id:redstone,Count:1,tag:{display:{Name:Point,Lore:[Point]}}},{},{}],DropChances:[0.085F,0.085F,2.0F,0.085F,0.085F]}

You also need a objective called point. /scoreboard objectives add point dummy Then you need a clock running the following commands in this order:

  1. scoreboard players set @e[type=Item] {Item:{id:redstone,tag:{display:{Name:"Point",Lore:[Point]}}}} point 1

  2. execute @e[type=Item,score_point_min=1,score_point=1] ~ ~ ~ scoreboard players add @p point 1

  3. kill @e[type=Item,score_point_min=1,score_point=1]

I would use this to summon in the custom mob you want. Hope this helps! If anything was wrong or anything was spelled wrong please tell me!