January 1 in the Western Rite of the Catholic Church is the Solemnity of Mary. This is the oldest Marian feast and celebrates her title of "Theotokos" (God-bearer) or "Mother of God". The Byzantine Rite celebrated this feast the day after Christmas. Today we don't just celebrate the existence of a Biblical character named Mary who happened to be the mother of Jesus--we celebrate Mary who made it possible for us to be children of God.
In the Byzantine Rite (and the Anglican Church), January 1 is the Circumsion of Christ. As per Jewish custom Our Lord became a child of the Covenant through this outward sign. This would be the first time Jesus spilled His blood. In addition it was His official naming.
Almighty God, who made thy blessed Son to be circumcised and obedient to the law for man; Grant us the true circumcision of the Spirit; that, our hearts and all our members being mortified from all worldly and carnal lusts, we may in all things obey Thy holy will; through the same Thy Son Jesus Christ our Lord. Amen (Collect for the Feast)
Saint Basil the Great is commemorated on January 1 too. He and his five siblings all became priests, nuns, and bishops in the fourth century; all became saints along with their parents. He established a monastic rule and formulated the Divine Liturgy used on 42 Sundays in the Byzantine Rite.
Working of miracles and gifts of healing are through the Holy Spirit. Demons were driven out by the Spirit of God. The devil was brought to naught by the presence of the Spirit. (St. Basil, De Spiritu Sancto 19:49)
As the art is potentially in the artist, but only in operation when he is working in accordance with it, so also the Spirit is ever present with those that are worthy, but works, as need requires, in prophecies, or in healings, or in some other actual carrying into effect of His potential action. (DSS 26:61)