His job is making sure that the company’s files are recorded properly, including files dealing with riba-based loans

Firstly: 

If your work
does not involve dealing with riba or approving it or helping with it, or
dealing with other haraam things apart from riba, then it is permissible
work and there is no sin on you if you continue it, even if the company
takes riba based loans or pays riba. But it is better to leave this job and
work for a company that is far removed from this great evil, because it is
established among the scholars that it is makrooh to engage in buying and
selling and renting etc with persons whose wealth includes haraam wealth. 

Secondly: 

It is not
permissible to write down riba or to document it. The one who does that is
cursed by the Messenger of Allaah (peace and blessings of Allaah be
upon him), as Muslim (1598) narrated that Jaabir (may Allaah be pleased with
him) said: “The Messenger of Allaah (peace and blessings of Allaah be
upon him) cursed the one who consumes riba, the one who pays it, the one who
writes it down and the two who witness it, and he said: ‘They are all the
same.’” 

Following up
on these documents and supervising them is haraam, because it is cooperating
in sin and transgression, and approving of evil. Allaah says (interpretation
of the meaning): 

“Help you
one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but
do not help one another in sin and transgression. And fear Allaah. Verily,
Allaah is Severe in punishment”

[al-Maa’idah 5:2]

What you
have to do is advise those who are in charge of this company to give up this
great evil. If they respond, then praise be to Allaah, otherwise you must
avoid recording and documenting riba, and keep away from everything that
involves helping in sin or approving of it. 

And Allaah
knows best.