Please give me correction

Having a class in the early morning, so sleepy.

I am not sure what your intention is with this sentence. Are you talking about a class that you are in right now? Or a class that you will attend in the immediate future?

If you are in class right now and feeling sleepy, how about - 

I am in class right now, and I'm so sleepy.

If it is a class that you are about to attend in the immediate future, try -

I have to attend class, but I'm so sleepy.

Pleasse give me correction

I suggest one more variant:

"Having a class EARLY IN THE MORNING IS RATHER A SLEEPY THING TO DO".

So, guys, how d'you like it? 

Native U.S. English speaker here. :)

Pleasse give me correction

I have a class early in the morning when I'm so sleepy.