Database
[{id:1,info:{NameEmployee_1:{age:33,work:"Yes",city:"LA",},NameEmployee_2:{age:12,work:"No",city:"NY",}}}]
Query
db.collection.aggregate([{$project:{obj:{$objectToArray:"$info"}}},{$project:{_id:0,obj:{$filter:{input:"$obj",as:"item",cond:{$eq:["$$item.v.city","NY"]}}}}},{$project:{info:{$arrayToObject:"$obj"}}},])