1

I’m not suore which of the two is correct......Me and Tessa’s Books or My and Tessa’s books ? Couldn’t find an answer in grammar books.

1

It's considered polite, and it's more commonly used in writing, to leave the first personal pronoun(s), such as I, and the possessive pronoun; mine, at the end.

For example,

My husband and I.

NOT

I and my husband.

Which is perfectly grammatical but no one says it.

Therefore, in the OP's situation it is preferable to say

Tessa's books and mine.
My brother's room and mine

OR

My books and Tessa's.
Our room (if you and a sibling share the same room)

0

The title and the question are different. I am answering the question.

It should be:

My books and Tessa's (books)

or you may say:

Tessa's books and mine.

becauseme is the objective case of I. here we are talking about the possession of books.

So we have to use the possessive case of I- my or mine.

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