No, there is no Prime Cohort in this time frame. I am not familiar with Rio's mod so do not know how he has set up the structure of the Late Roman Legions - basically, your main front line legions in this period were smaller than the Principate period. The latter were between 5,000 and 6,000 in terms of paper strength whereas the later field army legions from say Constantine onwards were around a 1,000 to 1,200 in terms of paper strength. These new legions were sub-divided into 5-6 maniples of around 200 apprx.
Cohorts existed still under the old legions which were now relegated to border static defense and down-graded in terms of pay and status. As a result, I would expect any old first cohort to have long ago been brigaged off as a separate unit or vexillation and now to be ensconced in a fort somewhere as its own independent unit.
Check
here for a more detailed breakdown I wrote a while back. Please not that I used the term 'ordo' to designate the 200 man sub-unit in a legion but that now I believe the term 'manipulus' to be the accurate one!