Does the emission of semen during the daytime in Ramadan while fondling the penis—without the intention of masturbation—count as intentional, and what is the expiation for that?

Masturbation is the deliberate expulsion of semen by any means, and it invalidates the fast when done intentionally. Therefore, you are obligated to make up the day you invalidated by masturbation, without expiation. You must also hasten to repent to Allah Almighty.