Mushoku no Tensei - Eris Gaiden

Synopsis:

Eris Boreas Greyrat is a previous honorable young lady, who one day was shipped to the opposite side of the world with her cousin Rudeus. She developed as a swordswoman, in any case couldn't save Rudy as he was anywhere close to killed. Concluding that she needs to be somebody who can uphold him instead of the opposite way around, Eris chooses to leave Rudeus and go on her own excursion. This is a side project of Mushoku Tensei, which splinters off from the fundamental manga at around section 51 (volume 6 of the light novel, first period of the anime).