I am sure someone will correct me if I am wrong but these are fairly common and the photos are good enough to attribute:
1. Constantine I "Campgate" AE3 Obv: CONSTAN-TINVS AVG - Diademed bust right, draped and cuirassed. Rev: PROVIDEN-TIAE AVGG - Campgate with two turrets and one star. Exe: SMTS / (epsilon) | Thessalonica RIC VII 169.1
I think the second one is:
2. Constantine II "soldier and standard" AE4 Obv: CONSTANTINVS IVN NOB C, laureate, cuirassed bust right. Rev: GLORI-A EXER-CITVS, two soldiers holding spears and shields with two standards between them. Exe: SMTSB | Thessalonica RIC VII 199
The ones you picture look real to me but I am not the end all on that, certainly there are not a huge glut of 4 dollar constantines but as mentioned before, there are some all the same. As for value they are very low and without doubt, they have probably been crusted with corrosion, cleaned, and probably retoned, certainly that will expose corrosion pits and marks. Cheap coins but many like these are attractive and interesting as well. They show how sophisticated (if not completely debased) the monetary system had become with complex mint marks, iconogaphy that had become standard, etc...all int he hopes of keeping the millions who used the system in coinage. Many mints, many different coinage being produced in each mint...it was more complex than most monetary systems today.
Here is an example of what I feel to be an exception example of a late constantine coin: