275 (c. not later than) birth of Theodora.
There is no true resolve as to the parentage of Theodora. Like the older text here, it has been most common to position Theodora as the daughter of Eutropia while the step-daughter of Maximian, thus of a now unknown paternity, and not of Maximian's blood line. In 1982, however, Timothy D. Barnes, in The New Empire of Diocletian and Constantine (Cambridge, MA: Harvard University Press, 1982), pp. 33-4, presents the case that Theodora may well have been the daughter of Maximian while the step-daughter of Eutropia. Since Theodora is the mother of all of Constantine I's half siblings, the only real bearing of Theodora's paternity is whether Maximian's blood line continued into the branch of the neo-Flavian dynasty comprising Constantine's half-brothers and half-sisters. For example, the ancestry of Julian the Apostate, the last ruling member of the neo-Flavians, goes for sure back to Constantius and Theodora, but beyond that he is directly related to either Eutropia or Maximian.
It is only speculation on the part of this author, but if it is indeed Maximian's blood, and not Eutropia's, that flows within Constantine's half-siblings, then this might explain why Constantine did not delegate high governmental posts to his half-siblings during his years as sole emperor.
For Maximian, one wife is attested, and another must probably be postulated. The Syrian Eutropia, who was still alive after 324 (Eusebius, VC 3.52, cf. Sozomenus, HE 2.4.6), bore him both Maxentius and Fausta (Origo 12; Julian Orat. 1, 6a; Epitome 40.12; Sozomenus, HE 2.4.6). It is normally believed that Eutropia had previously been married to someone else (often identified as Africanius Hannibalianus, cos. 292) and that Theodora, the wife of Constantius, was her daughter by her first husband, and thus the stepdaughter of Maximian. This view should be rejected. The writers who call Theodora the stepdaughter of Maximian (Victor, Caes. 39.25; Eutropius, Brev. 9.22; Jerome, Chronicle 225; Epitome, 39.2, 40.12) all derive their information from a single lost source written c. 337, whose testimony is not necessarily reliable. Other extant writers make Theodora the full daughter of Maximian; though fewer in number, they are superior in authority (Origo, 2; Philostorgius, HE 2.16a). Their evidence should be preferred on the general ground that, when no decisive evidence exists, normally reliable sources deserve credit over those whose inaccuracy can be detected on other matters. Moreover, if Theodora was the full daughter of Maximian, then a more natural meaning can be assigned to the panegyrist of 289, when he declares that Maximian has bound his praetorian prefect to him by a marriage which produces "non timoris obsequia sed vota pietatis" (Pan. Lat. 10(2).11.4): the allusion is to Constantius as his son-in-law, not to Hannibalianus as the first husband of Eutropia. (The passage is quoted and discussed more fully in Chapter VIII.1.) Hence Theodora was born no later than c. 275.
If Theodora was not the daughter of Eutropia, then she must be Maximian's daughter by a previous wife, whose name, origin, and existence are nowhere directly attested. It may be relevant, therefore that one of the sons of Constantius and Theodora was called Hannibalianus. That might indicate that Maximian married a daughter of Africanius Hannibalianus (cos. 292), one of whose ancestors appears to derive from Tralles.
The ages of Maxentius and Fausta are nowhere explicitly attested. Modern estimates for the date of Maxentius' birth have diverged widely, from c. 277 to c. 287, while the birth of Fausta has often been dated c. 298. But the latter date depends on the supposition that it was only in 298 or 299 that Maximian first visited Rome, where Fausta was born, according to Julian (Orat. 1, 5d). That premise is vulnerable. Probability, and the evidence of contemporaries, appear to indicate that Maximian's son and daughter were born c. 283 and in 289 or 290. The panegyric of 289, when interpreted strictly, seems to indicate that Maxentius has not yet reached his seventh birthday (Pan. Lat. 10(2).14.1: "felix aliquis praeceptor expectat"), while by 305 he was both married and a candidate for the purple (Lactantius, Mort. Pers. 18.9, ff.). Maxentius' mother, in November 312, swore that she had conceived him in adultery with a Syrian (Origo, 12); that might imply that Maxentius was born, or at least conceived, in Syria--where Maximian would have been c. 283, serving under the emperors Carus and then Numerianus. As for Fausta, a mosaic in the palace of Aquileia, whose dramatic date was no later than 296 (and may have been 293) depicted her as a girl (Pan. Lat. 7(6).6.2), and the panegyric delivered at her wedding in 307 appears to assume that she is already of child-bearing age (Pan. Lat. 7(6).2.1 ff.; cf. 6.2: "sed adhuc [i.e. in the 290s] impar oneri suo"). Moreover, if Fausta was indeed born in Rome while her father was there, then the evidence for Maximian's movements appear to render it probable that she was born in 298 or 290.
Timothy D. Barnes, The New Empire of Diocletian and Constantine (Cambridge, MA: Harvard University Press, 1982), pp. 33-4.
Further text relative to Eutropia not being the mother of Theodora:
Two Gallic panegyrics can be combined to render it highly probable that Constantius was praetorian prefect of Maximian for several years before his elevation as Caesar. The orator who addressed Constantius on 1 March 297 allides to his first appearance before maximian through the aid of Constantius: [Latin text]. He then speaks of his experiences in an office to which Constantius appointed him, when he apparently accompanied Constantius on a campaign before 293: [Latin text].
If Constantine could introduce the orator to the emperor's presence, make or secure him an appointment and conduct military operations, he must have held high office under Maximian. An earlier speech, delivered before Maximian on 21 April 289, has an allusion which is both less and more specific: [Latin text]. The most natural interpretation of the text is that Maximian has allied himself by marriage to his praetorian prefect. Two explanations of the allusion have been advanced: either the prefect is Afranius Hannibalianus, and it is argued that Maximian's wife Eutropia was previously married to Hannibalianus, or the prefect is Constantius, whose marriage to Theodora is implicitly dated to 293 by several narrative sources (Victor, Caes. 39.24; Eutropius, Brev. 9.22.1; Jerome, Chronicle 225; Epitome 39.2). The latter identification is correct. The date in these sources deserves no respect, for they derive from a single source written c. 337, which muddled the chronology of the 290s, and described Maximian's daughter Theodora as his stepdaughter. The reliable evidence indicates that Constantius was the praetorian prefect and son-in-law of Maximian by 288; the orator of 21 April 289 refers to a recent campaign waged by him against the Franks. Constantius presumably continued in office until he became Caesar in 293
Timothy D. Barnes, The New Empire of Diocletian and Constantine (Cambridge, MA: Harvard University Press, 1982), pp. 125-126.