A false gospel.

Pseudo means false or counterfeit.

No. Scholars have demonstrated that Mark's Gospel was written first, and that Matthew's Gospel was partly based on the contents of Mark's Gospel. Matthew's Gospel was originally written anonymously and only attributed to St Matthew later in the second century. However, scholars say that Matthew could not have been written by an eyewitness to the events it portrays.

The disciple Matthew did not write any of the gospels.