[{_id:123,data:1,details:[{item:"a",day:1},{item:"a",day:2},{item:"a",day:3},{item:"a",day:4}],someMoreField:"xyz"}]

db.collection.aggregate([{$match:{_id:123,"details.day":{$gt:1,$lte:3}}},{$project:{_id:1,details:{$filter:{input:"$details",as:"value",cond:{$and:[{$gte:["$$value.day",1]},{$lte:["$$value.day",3]},],},},},},},])