The subscription site Roots Ireland has a October 13 1820 baptismal record for a Mathew Mulcahy with father Denis Mulcahy and mother Mary Ryan in the Newport RC parish. The family lived in Ballyhourigan townland in Killoscully civil parish. There is a good possibility that this record is for your ancestor. Siblings John 1819 Mary 1823 Catherine 1828 Norah 1833.
Parents were married in Newport on May 23 1816. Denis was from Birdhill. Mary was from Ballyhourigan
The earliest Anne Ward baptismal record was in the 1830s so your Anne must have been baptized in a parish that no longer has records back to 1823/1824.