* 授業の後、残ってください (jugyō no ato, nokotte kudasai): This is a polite and formal way to ask someone to stay after class. It literally means "After class, please remain." This is suitable for most situations with a teacher.
* 授業の後、少し残って下さい (jugyō no ato, sukoshi nokotte kudasai): This is similar to the above, but adds "sukoshi" (a little), making it sound slightly less demanding.
* 授業が終わった後、話があります (jugyō ga owatta ato, hanashi ga arimasu): This translates to "After class is finished, I have something to talk to you about." This is suitable if you need to speak to the student privately.
* (先生に)授業後に残ってください。(sensei ni) jugyō go ni nokotte kudasai.: This means "Please stay after class (to the teacher)." Adding "(先生に)" makes it clear who the request is directed towards.
The best choice depends on the situation. If you're a student asking the teacher to stay, the first or second option is best. If you're a teacher asking a student to stay, the third option might be more appropriate. Remember to use polite language when speaking to a teacher.