Police are providing support to the family at the centre of the New Year's Day incident in Hamilton

A baby died, and a woman and baby were seriously injured, in the early morning incident in Fairfield.

A 34-year-old man -- who remains in a stable condition under police guard in hospital -- is due in court next month, charged with murder and attempted murder.

Hamilton Mayor Paula Southgate says it's a tragic start to the year for the city.

She says her thoughts are with family, friends and the Fairfield community.