"Hello everyone. This is just a story idea in which you can use.
In this story, after supposed "death" of Summer Rose, she finds herself on a verge of death in a forest around Konoha after a desperate battle against grim or human or both. Anbu or Naruto finds her after an incident in the village (Preferably Hinata's kidnapping attempt or Uchiha Massacre for Anbu or Mizuki defection attempt, after Chunin exam invasion, after Pain and Naruto battle of village, or during the war for both either Anbu or Naruto). Due to finding her not in an ideal situation, the village held her captive and interrogated. Summer and Naruto gets to know more of each other, whether or not Naruto was ordered to get information from her is up to you. After multiple talks Naruto starting to question where he actually from and his heritage. After the last battle of the fourth great shinobi war, war hardened, grey, and almost emotionless Naruto busts out Summer from the captivity preferably against Hokage wishes, but can also can do with Naruto convincing the Hokage to let her out. Naruto will be accompanying Summer back to her
On the journey, Naruto will be learning value of family, and life, where a person should cherish every moment with someone they love before they are gone. Naruto will also will be learning to move on of death of loved one. While Summer would learn that the world and reality can be far more Machiavellian then her slightly standard fairy tale view. Naruto and Summer would face many challenges and hardships in their 3 –5 years travel. (Preferably the travel includes elements or scenes from "The last of us", "Gladiator", "The Last Samurai", "Mummy: Tomb of the Dragon Emperor", "Matrix", "I Robot", "Bleach", "D-Gray Man", "Assassin's Creed", "Stargate", and "Gundam Seed". And/Or you can make your own bonding situations.) Along the journey to Remnant, Naruto finds out that he is genetic enhanced (faster, stronger, more flexible, more durable, better reflexes and higher metal capacity then humanly possible. Think of coordinator from "Gundam Seed". There is also an option where a very rare mutation where Naruto have multiple faunus features of various animals due to multiple faunus genes from his unknown ancestor) being from Summer, Raven, and Taiyang. 3 to 4 years before Yang's birth, Taiyang couldn't decide between Raven and Summer so all three agree to have Naruto through new scientific means. However, due to unfortunate events and circumstances, Naruto ended up in Konoha and adopted by Minato and Kushina, after few weeks or months after Naruto's birth. Just before arriving at Remnant Summer learns that Naruto is actually her son.
From here you have three basic options.
Option 1:
When they come Yang and Ruby (Age 17 15 respectively) just beginning to enter Beacon, while Naruto (Age 20-21) start to integrate with family and far less dangerous and more positive atmosphere and society. Due to Naruto superb combat, tactical and some political skills, Ozpin recruits Naruto as a teacher or at least an assistant teacher at Beacon. Naruto joins the protagonist to stop Salem.
Option 2:
When they arrive at Remnant, they come upon unfortunate circumstances where they being chased by authorities and they come to Taiyang's house and before Summer could introduce Naruto to him, Naruto are gone to divert the attention of the authorities away from Summer and her family and left a letter. In the letter he would explain that he is their son (Summer didn't know until the letter, she thought of adopting him), and shows some paper work he found to prove it, and how Konoha is his place even though they are his biological family. Naruto arrives at Konoha and knowingly he would be executed due to leaving the village on negative circumstances. Just before his life ends, his family and friends he had made on his journey (some very powerful figure) to stop the execution, and killing Naruto would be either an act of war or make their village under very difficult situation. There is an option to continue with Option 1.
Option 3:
Naruto and Summer when Beacon during the attack of Vytal Festival. Summer went into a coma and due to misunderstanding Naruto family and some main characters think that Naruto had cause Summer harm and about to kill her. Naruto escapes and while in hiding from his family and authorities, tries to clear his name at the same time trying to spoil Salem's plans and take down her and her associates. At the end of Salem situation, Naruto help the protagonist fight in the final battle and left to Konoha after it was over. Summer wakes up from her comma and Option 2 starts but minus the letter and Summer knows Naruto relationship to her before the arriving to Remnant. Naruto's family trying to fix the relationship from the misunderstanding.