[{"id":1,"name":"N1","tasks":{"project1":{"task7":{"count":10,"time":1.2},"task3":{"count":56,"time":1050}},"project25":{"task7":{"count":25,"time":10}}}},{"id":2,"name":"N1","tasks":{"project1":{"task70":{"count":10,"time":1.2},"task3":{"count":56,"time":1050}},"project25":{"task70":{"count":25,"time":10}}}},{"id":3,"name":"N1","tasks":{"project1":{"task70":{"count":10,"time":1.2},"task3":{"count":56,"time":1050}},"project25":{"task7":{"count":25,"time":10}}}}]

db.collection.aggregate([{$project:{_id:0,tasks:{$objectToArray:"$tasks"}}},{$match:{"tasks.v.task7":{$exists:true}}},{$project:{tasks:{$arrayToObject:{$filter:{input:{$map:{input:"$tasks",in:{"k":"$$this.k","v":"$$this.v.task7.count"}}},cond:"$$this.v"}}}}}])