Since you’re talking about [some of] us (first person plural), your subject and verb must agree in person and number, and if the object maps one-to-one with the subject (e.g., each person has one job, not one job shared among multiple people), it should also agree in number - thus, I’d say our jobs: A quarter of us will lose our jobs. If you need/want the “going”, A quarter of us are going to lose our jobs.
It has been argued that “A quarter...” makes it a singular subject; I (and those that share my linguistic environment) disagree: The basic subject is plural, us. If we start from that, we get We (All of us) are going to lose our jobs. But it's not all of us: Some of us are going to lose our jobs. The subject is still plural. Changing some to a specific amount - a quarter - doesn’t change the number of the subject; it's still plural, A quarter of us, thus: A quarter of us are going to lose our jobs.
If the subject were to change to One of us, then the verb would become singular - One of us is going to lose his/her/xir job.