Database

[{"productionYear":1},{"productionyear":1}]

Query

db.collection.find({$expr:{$gt:[{"$size":{"$filter":{"input":{"$objectToArray":"$$ROOT"},"as":"kv","cond":{"$and":[{$eq:[{$toLower:"$$kv.k"},"productionyear"]},{$eq:[1,"$$kv.v"]}]}}}},0]}})

Result