Although the Child isn't a younger-version of Yoda himself, he was given the name by the Internet, due to him being the same species. Numerous people have called the Child the biggest character of 2019.
The Mandalorian accepts the mission of tracking down and capturing a 50-year old target. Future on the Mandalorian ends up finding the target, which was revealed to be the baby which is the same species as Yoda. In the second episode, the Mandalorian gets attacked by a rhinoceros-type creature, which was about to kill the bounty-hunter, the Child uses The Force to levitate the creature, helping the the Mandalorian to kill the creature. Later on, the Mandalorian ends up giving the Child to the Client. The Mandalorian asks the Clients plans on what will he do to the Child, but the Client just responded that it isn't his concern.
The Mandalorian ends up infiltrating the Cilent's base and retrieves the Child, which got studied by a Doctor. The Mandalorian ended up getting ambushed by other bounty hunters which were forcing the Mandalorian to give them the Child. The Mandalorian was able to escape when unexpectedly other the Mandalorians arrived to the location attacking the bounty hunters, letting the Mandalorian escape with the Child In the 4th Episode, the Mandalorian arrives to a planet with the Child to get as far away from the bounty-hunters. The Mandalorian wanted to take care of the villagers on the planet, but a bounty hunter appeared on the planet wanting to take the Child, to which the Mandalorian again had to retreat.
In 5th episode, the Mandalorian joins a aspiring bounty hunter to capture an assassin. Eventually, the bounty hunter ends up taking the Child hostage, at which point the Mandalorian kills him and gets the Child back.