Your great grandfather was born in Jan. 1856, and conditionally baptized March 1856. The Catholic Church, and the other major Christian churches, teach that you can be baptised only once. The recognised form of baptism is that there is the intention to make the person being baptised a member of the Christ's Church, that water is poured over the head of the person, and that the words state 'I baptise you in the Name of the Father and of the Son and of the Holy Spirit'. Your note suggests to me that GGF was baptised at home as a sickly new born child by some one other than a priest. Then when he was well enough he was taken to church. The priest at Troy was told what had happened but he was not sure that the baptism was performed in the correct way. He recognised that the baptism may have been valid, so he commenced the service with the words 'If you are not already baptised, I baptise you ...' and performed the Baptism rite. If GGF had been validly baptised at birth this rite would not have had any effect; it was just to make sure. The child would then have received all the other ceremonies and prayers that are part of the church ceremony but are not essential to being baptised. Sometimes only the additional prayers and ceremonies are performed and then the entry is annotated with the words "ceremoniae suppletae" or similar, meaning that the early baptism was known to be valid and the child just received the extra prayers and ceremonies. This also happens in the Anglican / Episcopal(?) Church where you may find the words 'received into church'

Hope this helps
Jim Lancaster (Bury, Lancs., England)