What is wrong in the following sentence?
"As I am tired so I shall sleep early tonight."
It seems alright to me but apparently it has an error somewhere.
I would not word it this way (as you did in your comment in another answer):
We cannot use a 'so' after an 'as'.
Both of those words are flexible words with different usages, and a "rule" like that will likely get you into trouble.
Here's the problem with the sentence in your question. In that context, the first word (as) is being used to essentially mean 'because', and the second (so) is being used to mean 'therefore'. That's why the repetition doesn't work. Does this sentence look okay to you?
Because I am tired therefore I shall sleep early tonight.
(Perhaps the awkwardness off that structure is more glaring when we use the bigger words.) No, instead we'd say one of the following:
You'd use either
As I am tired I shall sleep early tonight.
I am tired so I shall sleep early tonight.