According to Cedrenus (Histor. Compend. 1566 p. 205) Justin's Treatise against all heretics was written in the reign of Hadrian, and this opinion is probably correct, for Justin refers to the work in his larger Apology, which was composed soon after the accession of Antoninus Pius. [Karl Gottlieb Semisch, Justin p. 48]
Justin habe sein Syntagma gegen die Haeresieen unter Hadrian geschrieben und sei, wie Polykarp und Dionysius von Korinth, unter Pius Märtyrer geworden, nicht nur acceptirt, sondern auch geneigt ist, sie auf die Hypotyposen des Clemens zurückzuführen. [Harnack Geschichte der altchristlichen Litteratur bis Eusebius. Theil 2 p. 282]
FWIW Epiphanius says explicitly that Justin was martyred under Antoninus Pius:
Epiphanius distinctly places an event subsequent to Justin's death in 149 or 150 : and Cedrenus and Glycas send us back to the reign of Antoninus Pius. Epiphanius's authority is unknown, but there is no reason to suppose it identical with that of Cedrenus (whom Glycas very possibly follows) ; for the one wrote about Tatian. and the other about Justin. Further, as we have already seen, no less a personage than St Clement may be the source of Cedrenus's account. Thus we have in favour of the reign of Antoninus Pius two distinct traditions, in favour of that of M. Aurelius only the one long Eusebian tail, suspended ultimately not, as far as we can see, from any earlier author or tradition, but from the historian's private interpretation of a passage in Justin's own second Apology ... Accepting then from Epiphanius 149 or 150 as the posterior, or rather post-posterior, limit of Justin's life, his first Apology must fall between 138 and that time. It is best to place it tolerably near to 148 or 149 ... Accordingly we may without fear of considerable errour set down Justin's first Apology to 145 or better still to 146, and his death to 148. The second Apology, if really separate from the first, will then fall in 146 or 147, and the Dialogue with Tryphon about the same time. [Fenton Hort The Date of Justin Martyr, The Journal of Classical and Sacred Philology, Volume 3 p 190]
dating back to conversations with his grandfather, Gaston Frank. "He said we represent one of the last descendants of the Frankist Jewish faith in the world," he muses. "I grew up thinking that our family was something like the Last of the Mohicans."