‘And the maid saw him and began again to say to those who stood by, “This is one of them.” But he again denied it.'
As she moved around ‘the maid' (or another maid. The definite article might be a Semitism) spotted him and her suspicions were again aroused. Possibly she had been prompted by the first maid. So she said to those who stood round, “This is one of them”. This was her moment and she was not going to lose it. It would seem that she deliberately spoke so that Peter would hear. And he again denied it. This time the denial was more specific and more general, ‘he went on denying it'. And his uneasiness was turning to fear. Yet he still would not leave. There is here a distinct contrast with the dignified way in which Jesus was dealing with His accusers.
‘The maid.' In Mark this appears to refer to the same maid, but not necessarily so. The definite article may be a Semitism and therefore not to be seen as so emphatic. It may simply indicate ‘the maid, that is, the one who now saw him'. Matthew and Luke tell us it was ‘another'. ‘Again' then simply means that there was a further accusation.
‘He again denied it.' Slightly more emphatic.