Menu alter for a particular content type I am trying to add a custom access callback for the node edit page for a particular content type. 

I am using alterRoutes function to change the access callback but I am unable to get the node type in this function. 

Am I missing something obvious?
There are o node type specific edit routes, only one. You'd have to alter that and then in your access callback, decide if it is your node type or not.

But, why don't you just implement hook_node_access() and check for the update operation? That allows you to control access to that page and also any edit operation elsewhere on th system, on whatever condition that you want.