According to new legal docs obtained by TMZ ... Jason filed trademark paperwork for the phrase "Aloha J" with the intent of using his favorite saying for advertising, marketing and communications services ... mainly over the internet and on social media.

The "Aquaman" star is staying true to his Hawaiian heritage ... he's been signing off his social media posts with "Aloha J" for quite a while now, and it's kinda become his own little saying. Now, he wants to turn his slogan into financial gain.

Jason wants to lock down the rights to "Aloha J" for all sorts of 21st-century marketing methods ... including search engines, mobile phones, blogs and anything that goes viral. Ya know, things the ancient Hawaiians never dreamed of.

If the application gets approved, we're guessing Jason will send a big "mahalo" to the trademark office.