What's Jump Rookie?
「次世代のWEBマンガはココから生まれる!!!」 So claims the mission of Jump Rookie, a label by Shueisha meant to collect and distribute manga work by mangaka hopefuls and perhaps kickstart their career with an eventual serialization in Shonen Jump or any number of Shueisha's other publications.
Jump Rookie's current incarnation is a website and associated smartphone apps for Android and iOS that readers can use to read its selection of manga for free. The platform touts itself as friendly to creators as well as consumers, and clear effort has been put in to make publishing your manga to Jump Rookie (ostensibly) easy and accessible.
Jump Rookie isn't just a Shonen Jump spin-off and has manga from all genres and demographics. The website and all of its manga are naturally in Japanese, which is to be expected when reading fresh manga straight from the tap.
Who is Akagi Kei?
Akagi Kei (赤木 継), whom you may know from their work on Koi no Yamai (恋の山井, not to be confused with the unrelated Morino Megumi's Hananoi-kun to Koi no Yamai) published in Kodansha's Evening magazine, has published two new manga series on Jump Rookie within the last two weeks, marking their advent to the platform: Assassination Hospital (アサシネーションホスピタル) and Nande Ima Kokuhaku Surundayo (なんでいま告白するんだよ)
The second chapters of both manga have been released just this past weekend, so let's take a moment to spotlight these brand-new works.
Assassination Hospital

Family drama, intrigue, and a dash of dry humor makes Assassination Hospital worth a look for those searching for their next battle manga.
Nande Ima Kokuhaku Surundayo

This one's my personal favorite of the two, and a real treat for those who enjoy some self-aware jokes about lovecome genre conventions.
Outro
If either of these manga interest you, they can be read for free via Jump Rookie through the provided links. Akagi Kei also publishes new pages to upcoming chapter of their manga on their Twitter account at @nougekanow, so those who are particularly invested in the next developments in either manga can get an advanced look there.
I just want to put something out there while these manga are still brand-new, so more people might have the opportunity to read. Through whichever avenue, may you read some good manga today.