Shōnen Jump series that might interest
One Piece - The current big daddy of manga, bigger than Dragonball and not underserved. Close to 1000 chapters now though so I'd highly recommend reading with a subscription or going to the high seas.
My Hero Academia - After One Piece this is probably the second most popular traditional battle shōnen overall, the author has found it hard to keep the page count up of late but the quality has remained high for the most part.
Demon Slayer: Kimetsu no Yaiba - Fantastic series following the exploits of Tanjirō Kamado as he tries to find a cure to a demons curse. It is currently building towards its climax and has an anime set to begin in April.
The Promised Neverland - A battle of wits in a world which at first seems just a bit too perfect. Recently received the anime treatment which has further bolstered its popularity.
Dr. Stone - A Mysterious phenomenon changes the world in the blink of an eye. What happens when a genius wakes up in a stone age world and tries to reclaim what was lost? Currently my favourite weekly series with a good mix of action, humour and mystery. Anime is coming later this year.
Jujutsu Kaisen - It didn't click for me within the first 10 chapters I read, but I've heard that it's improved massively since and 'ranks' well in the Table of Contents with good sales to boot. Definitely one to watch.
Hunter X Hunter - One of the best battle shōnen's and probably the most consistently great. Held back by repeated hiatuses due to it's author being in poor health.
Chainsaw Man - Pretty much what it sounds like. There is promise there and the author has hit gold in the past with Fire Punch but it's yet to do much for me.
Black Clover - Generic battle shōnen, it has its moments but otherwise it's a by-the-numbers series that somehow manages to sell well.
Boruto: Naruto Next Generations - A continuation of the Naruto story. New author and artist while Naruto creator Masashi Kishimoto advises.
Food Wars: Shokugeki no Sōma - Chefs battle it out in the kitchen in an over-the-top fashion. Quality was excellent for much of the run though the latest couple of arcs have been a big let down.
Weekly Shōnen Magazine series that might interest
The Seven Deadly Sins - Fun battle shōnen with a large cast of likeable characters. It's currently in the middle of what could be the final battle and the quality has remained largely consistent.
Edens Zero - Sci-fi battle shōnen from the author of Rave Master and Fairy Tail. I loathed Fairy Tail but so far this has been a very enjoyable series.
To You, The Immmortal - Not one I've read much of but have heard nothing but good things and it is quite highly rated.
Fire Force - Firefighter battle shōnen, starts of a little rough but develops into a decent series after a few volumes.
Other series to check
JoJo's Bizarre Adventure - My all-time favourite series. Battle shōnen/seinen following the Joestar family and friends as they battle the supernatural with their wits and fists, then later with complex supernatural abilities of their own. Going strong for over 30 years and 8 parts, currently has Part V airing as an anime.
Berserk - Dark Fantasy/Supernatural series following the life of Guts. One of the best ever manga series with gorgeous art only let down by its author's frequent hiatus breaks.
I Am A Hero - Society has fallen to zombie-like monsters. Follows a man not quite in touch with reality as he tries to survive.
Mob Psycho 100 - Psychic fights and ghostbusting with a MC you can't help but grow to love, one of the best series of recent years and the second season of the anime is currently airing.
One Punch Man - Gag battle manga from the same author as Mob Psycho 100, has a redrawn version by the uber-talented Yusuke Murata which the anime is based on.
Zetman - Dark sci-fi about the rivalry of a genetically altered human and a gifted man with access to cutting-edge technology. Both try to do what they think is right in a corrupt and often bloody world.
Vagabond - Based on the life of legendary Samurai Miyamoto Musashi, features absolutely gorgeous art but the release schedule is inconsistent.
Kingdom - I'm currently making my way through this as we speak. It's set during the Warring States period of China and tells a fictionalised version of unification under the Qin dynasty of Ying Zheng.
The Lucifer and Biscuit Hammer - Sometimes bonkers battle series with some inventive abilities.
Gintama - Action and comedy aplenty, many chapters to read through or an anime to enjoy.
Gunnm/Battle Angel Alita - Classic cyberpunk goodness, recently got a movie which was flawed yet enjoyable.
Death Note - A battle of wits with a notepad that can kill whoever's name is written in it.
Gantz - Sci-fi horror where recently deceased people are brought back and forced to fight aliens and other nasties.