Jesus spoke with a Galilean dialect of Aramaic.
The following is not meant to be an answer specific to the question, but may help in some research on the subject:
The Syro Malabar and Syro Malankara rites of the Catholic Church in Kerala, India, which attribute their origin to St Thomas the Apostle, used to have their liturgy in Syrian language upto the 1950s after which the liturgy adopted the native language Malayalam as its medium. In fact you will find many short prayers still said in Syrian languae as a part of the liturgy. Besides the Catholic groups, the Catholic Orthodox Churches of Kerala also extensively use Syrian prayers during the liturgical celebrations. How close the phraseology of those prayers are to the dialect used by Jesus, can be commented on by Syrian scholars only.