Not nearly as well known as any of the others, Matthias was the apostle chosen to replace Judas after he betrayed Jesus and committed suicide. Matthias wasn't chosen by Jesus and isn't even mentioned in the synoptic gospels. Instead, he was chosen by casting lots after Jesus reportedly ascended to heaven. After being chosen, Matthias disappears completely from the New Tesament canon and isn't mentioned in any other reliable historical records.
The choosing of Matthias is depicted in the first chapter of Acts:
So they proposed two men: Joseph called Barsabbas (also known as Justus) and Matthias. Then they prayed, "Lord, you know everyone's heart. Show us which of these two you have chosen to take over this apostolic ministry, which Judas left to go where he belongs." Then they cast lots, and the lot fell to Matthias; so he was added to the eleven apostles. [Acts 1:23-26]
There's no information about who Joseph Barasabbas was, or why either of them were candidates for becoming an official member of the Twelve Apostles. It's not even clear why there was a need to replace Judas in the first place, unless it was for the sake of maintaining the symbolism of twelve, the number of the original Hebrew tribes. According to Clement of Alexandria:
Not that they became apostles through being chosen for some distinguished peculiarity of nature, since also Judas was chosen along with them. But they were capable of becoming apostles on being chosen by Him who foresees even ultimate issues. Matthias, accordingly, who was not chosen along with them, on showing himself worthy of becoming an apostle, is substituted for Judas. [Stromateis vi.13]
A medieval Greek historian claims that Matthias was crucified in Colchis, an area of the Caucauses, but there is no independent evidence of this having really occurred. Another Christian legend claims that Matthias was stoned then beheaded by Jews in Jerusalem.
Clement of Alexandria quotes a single sentence which he attributes to a Gospel of Matthias, but that's the only piece of the document which remains. There are also mentions of the existence of this gospel in Origen, Eusebius, and Jerome. Given how many gospels were created and attributed to various apostles and other companions of Jesus, it's likely that a Gospel of Matthias existed. Since Clement died in the early 3rd century, this could have been a relatively early gospel.