Is there any manga series which main character being falsely framed for things he/she didn't do and caused everyone to hate the main characters.

Or any manga that main character willing to self sacrifice and bare the things he didn't commit.

Rokkon Shojo
TeppenMezashiteTondeAruYo
Let justice be done, though the heavens fall

Boku no Namae wa "Shounen A"

Read it..Thanks
Any other recommendations?

Rokkon Shojo
TeppenMezashiteTondeAruYo
Let justice be done, though the heavens fall

May be give this one a try. It fits both of your requests in a way.
Sugar Dark - Umerareta Yami to Shoujo

Haven't read it yet. Awesome. Thank you

Rokkon Shojo
TeppenMezashiteTondeAruYo
Let justice be done, though the heavens fall

Hope, you'll enjoy it. I remember it being one of my favorites.
Also, you probably know, but just in case, there's a "Framed" categorie with 7 pages of titles, somewhere among them may be something that will meet your expectations.

Yup, I read it and enjoyed it. A bit short but happy ending. Might try the LN.
Would also try the frame categories.
However, if you have other recommendations, feel free to let me know.
Thanks

Rokkon Shojo
TeppenMezashiteTondeAruYo
Let justice be done, though the heavens fall