Database
[{"Array1":[{"Array2":[{"name":"6666","Array3":[{"_id":128938120,"nest":"samsung"},{"_id":12803918239,"nest":"nokia"}]},{"name":"5555","Array3":[{"_id":48102938109,"nest":"iphone"},{"_id":501293890,"nest":"micromax"}]},{"name":"4444","Array3":[{"_id":93801293890,"nest":"zen"},{"_id":571029390,"nest":"idea"}]}],"name":"old apartment"},{"Array2":[{"_id":410923810,"name":"3333","Array3":[{"_id":48102938190,"nest":"airtel"},{"_id":48102938190,"nest":"jio"}]},{"_id":41092381029,"name":"2222","Array3":[{"_id":10293182309,"nest":"master"},{"_id":38190238,"nest":"cub"}]},{"_id":83102938109,"name":"1111","Array3":[{"_id":810923810,"nest":"lect"},{"_id":20938904209,"nest":"dell"}]}],"name":"new apartment"}]}]
Query
db.collection.aggregate([{$project:{Array1:{$map:{input:{$filter:{input:"$Array1",as:"a1",cond:{$eq:["$$a1.name","old apartment"]}}},as:"a1",in:{name:"$$a1.name",Array2:{$map:{input:{$filter:{input:"$$a1.Array2",as:"a2",cond:{$eq:["$$a2.name","6666"]}}},as:"a2",in:{name:"$$a2.name",Array3:{$filter:{input:"$$a2.Array3",as:"a3",cond:{$eq:["$$a3.nest","nokia"]}}}}}}}}}}}])