Will Dorcena failed to submit the required 3,000 signatures and will not make the ballot for this fall’s mayoral election, election officials said Friday. Dorcena gathered roughly 2,131 signatures, officials said. In a telephone interview, Dorcena disputed the count and said, “I definitely have enough.” Sixteen people submitted a substantial number of nomination papers to run in the Sept. 24 preliminary election. Four candidates have had signatures certified by election officials and will appear on the ballot: city councilors Felix G. Arroyo and John R. Connolly; Suffolk District Attorney Daniel F. Conley; and state Representative Martin J. Walsh. Election officials will continue to tally signatures of the remaining 11 potential candidates.