Shinseiki Evangelion: Shito Ikusei (新世紀エヴァンゲリオン シト育成), translated as "Neon Genesis Evangelion: Shito Training", is a Japanese video game for the WonderSwan which was developed by Soft Machine and published by Bandai on July 22nd 1999. It is based on the Evangelion anime series.
This game has virtual pet elements to it, similar to a Tamagotchi. You play as Ryoji Kaji and you are tasked with taking care of Adam (or "Shito" as it is named in the game) in an embryonic state. You'll be able to make it evolve through different options ("Energy" to control its level of energy, "LCL" to control the different parameters of the amniotic fluid, "AT Field" to increase Shito's energy shield, and "Item" to give medicine to Shito). It will evolve into different forms depending of its stats. You can then make it battle the three Evangelions of Shinji, Rei and Asuka.
You can also explore different places from the anime as Kaji himself, talk to different characters and acquire different items for Shito. Once you finish the game, a special game mode will be available to make Shito battle at will.
Source: Evangelion.Fandom, "Shinseiki Evangelion: Shito Ikusei", available under the CC-BY-SA License.