Database
[{districtId:"xkj1",students:[{studentId:"123",type:"college"},{studentId:"124",type:"highSchool"}]}]
Query
db.collection.aggregate([{$project:{districtId:1,firstCollegeId:{$first:{$filter:{input:"$students",as:"item",cond:{$eq:["$$item.type","college"]}}}}}},{$project:{_id:0,districtId:1,firstCollegeId:"$firstCollegeId.studentId"}}])