One of the popular tropes in Persona fanfiction is 'alternate reality'. Writers like to explore what would happen if the events in the game took a different turn. In Highschool DxD, the 'rivalry' trope is common, especially between different devil clans. In a fanfiction that combines both, a trope could be 'culture shock'. A Persona character coming into the Highschool DxD world would experience a huge culture shock due to the different rules, species, and social structures. And also, the 'mentor - mentee' trope could be used. Maybe a powerful character from Persona becomes a mentor to a young devil in Highschool DxD, guiding them through their power - up journey.
In Highschool DxD OC fanfiction, the 'Power - Up' trope is quite common. Your OC starts with a certain level of power and then, through training, battles, or special encounters, they gain more power and become stronger. The 'Redemption' trope can also be used. If your OC has made mistakes in the past or has a dark history, they can strive to redeem themselves throughout the story. Also, the 'Chosen One' trope works well. Your OC could be the one chosen to save the supernatural world from a great threat, like an impending war between devils, angels, and fallen angels. This gives them a sense of purpose and importance in the story.
One popular trope is the 'Fish out of Water' scenario. For example, a character from Prototype suddenly finding themselves in the Highschool DxD world full of devils, angels, and other supernatural beings. It creates a lot of comical and interesting situations as they try to adapt.
In these fanfictions, the 'loner - with - a - heart - of - gold' trope is seen a lot. The OC mercenary acts tough and independent on the outside but has a kind heart deep down. The 'rivalry' trope is another one. They might have a rivalry with another character, which could be over power, status, or a love interest. And the 'hidden - potential' trope is also popular. The mercenary initially seems like an ordinary fighter but then reveals amazing hidden powers as the story progresses.
A great trope is the 'unexpected power - up'. Your female OC might be in a difficult situation, and suddenly, she discovers a new power within herself that helps her turn the tables. The 'protector' trope is also good. She feels the need to protect someone or something in the Highschool DxD world, like a group of innocent humans or a sacred place. And the 'identity crisis' trope can add an interesting layer to her character. She might be confused about whether she belongs to the devil side or the angel side, or something else entirely, and this internal struggle can drive the story forward.
In 'Persona 3 and Highschool DxD fanfiction', a cool crossover might involve the social links in Persona 3 being related to the relationships in Highschool DxD. For instance, the friendship between the characters in Persona 3 could be paralleled with the bonds of loyalty among the devils in Highschool DxD. Also, the Velvet Room in Persona 3 could have some sort of connection to the magic and power systems in Highschool DxD. It could be that the Velvet Room attendant has some knowledge about the devil fruits or the sacred gears in Highschool DxD.
A less common but still interesting trope is the 'reversal of roles'. In some fanfictions, Issei might find himself in a world where his devil powers are seen as something different or even feared in a new way. Maybe in a world of pure angels, he is the outcast and has to prove himself not to be an evil entity. This trope allows for a lot of character exploration and development for Issei.
The crossover element itself is a huge trope. Combining the unique worlds of Naruto, Highschool DxD, and the concept of ghouls allows for all kinds of interesting scenarios. Such as when the different magic systems and ninja techniques interact. For instance, a character might try to use a jutsu in the world of Highschool DxD or combine a devil's power with a ghoul's ability.
Rias from Highschool DxD is likely to be a popular choice in crossovers. Her status as a powerful devil and her leadership role can make for some exciting scenarios when combined with the Persona 3 universe. Another popular character could be Aigis from Persona 3. Her robotic nature and combat abilities can be quite interesting when pitted against the supernatural beings in Highschool DxD.
Issei is often a very popular character. His pervy nature and his growth as a character in the original Highschool DxD series make him stand out. In the fanfiction with Persona and gamer elements, his ability to adapt to new powers and situations can be really interesting to explore.
Another idea in the crossovers could be the exchange of technology or magic. The Velvet Room from Persona might have some connection to the magic system in Highschool DxD. Maybe the Velvet Room attendant could offer some insights or tools to the characters in Highschool DxD, like a special artifact that helps in controlling their powers better.