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I think the word you're looking for is period.
I have English for 1st period, Maths for 2nd period and Science for 3rd period.
Sixth Period Even Stevens the Musical
I'm not sure if 'hour' is incorrect, but I so far haven't heard at least in American English. Maybe in British English they say hour?
Updates based on comments:
No, in the UK we too use the word "period" – Peter Jennings
You might also use "block", if there are fewer ...periods....during the day. I'd say that might be more common in high school/college than lower schools, since there are typically fewer slots as the classes tend to be longer. – BruceWayne
At my high school in Michigan in the 2000s, class periods were always called "hours" instead of "periods." Maybe it varies somewhat randomly. –
To me (Australian ESL), "block" would suggest a time slot which is usually/normally/etc multiple periods; eg. if there are 2 periods before recess, one might say "morning block" to refer to periods 1 and 2 collectively, perhaps on a day with a special program, or a year level which uses them for double periods, or in contexts where the lessons themselves are not directly relevant. – Jiří Baum
At my high school in New York, class periods were 40 minutes with 5 minutes for changes between classrooms, so we definitely would not have said "hour". – David K