Three notes: First, your original sentence has the wrong article. Second, your additional sentences aren't using same properly (it's a weird word). Third, there are a couple ways to make this one sentence. See below.
First, note that the constructions you're using use the definite determiner/article (
books. So, instead of:
I have 4 bags. In each bag, there is a same book.
One would say
I have 4 bags. In each bag, there is the same book.
This is because the books have been mentioned before (in the first sentence of the example). See the Wikipedia page on definiteness.
Secondly, with your second sentence, the syntax of counters in English can be weird. For instance, the following is good:
I have 4 books.
But this is not good:
I have 4 same books.
This is because words preceding same require of the:
I have 4 books.
I have 4 of the same book.
I have ten dolls.
I have ten of the same doll.
Note also that nouns modified by of the are singular (book vs books)
Third, as you note, your original sentence sounds weird because it is strange to say something simple like it in two sentences. As others have pointed out, you could say something like:
I have four bags, each with the same book
However, this is also somewhat weird because you're emphasizing
bags without discussing the book much. The bag sounds more important because it is first, but there isn't much about it. So, if the book is more important, I would say something like:
I have four copies of the same book in each of these bags.
I have four of the same book with each in a bag.
I have a copy in each of these four bags.
I would expect to hear
I have four bags, each with the same book at a convention or something similar where people are getting free books in bags, and each bag might have a different book. So, if you're emphasizing you have four bags, but complaining you have the same books, then this sentence would be used.