Use $filter aggregation
Selects a subset of the array to return based on the specified
condition. Returns an array with only those elements that match the
condition. The returned elements are in the original order.
db.test.aggregate([
{$match: {"list.a": {$gt:3}}}, // <-- match only the document which have a matching element
{$project: {
list: {$filter: {
input: "$list",
as: "list",
cond: {$gt: ["$$list.a", 3]} //<-- filter sub-array based on condition
}}
}}
]);