I have an issue where I need to setup a router for area 1 but it will be connected to 2 area 0 routers
Essentially it will be area 0 <--> area 1 <--> area 0, and both area 0 routers will not be connected to each other in anyway. Is this something that is possible?
You cannot really have a discontinuous ospf backbone, well not recommended anyway apart from network merge proposes in this case a virtual link would be required
We need a better understanding of the topology of this network, especially we need to understand more about the topology of area 0. It is quite possible for a router in area 1 to connect to 2 routers in area 0. We do that all the time and call it redundancy and consider it a good thing. And it is not necessarily required for the 2 area 0 routers to be connected to each other. What is required, as Paul indicates, is that area 0 is contiguous. This means that the 2 area 0 routers have a way to communicate that goes through area 0. For example if there is a third router in area 0 and that third router connects to both of the 2 area 0 routers then things are good. But if the network is really literally as the original poster describes it
area 0 <--> area 1 <--> area 0
then Paul is correct that this is a discontiguous backbone and would be a broken implementation of OSPF.
Note that saying that it is a broken implementation does not mean that if you try to configure it that you would get error messages. You could configure it and the routers would accept the configuration. But you would find unexpected behaviors.
Agreed with @paul driver you may need sham-link, but that is not advisable in production environment, never seen personally in big production environment use case.
Actually, I have two solutions for you but both are not advised on your case. It's not a mean that it can't configurable.
Solution 1:- Create Virtual Link between Both ABR. (Most recommended)
Solution 2: If Area 1 is stub area then you can configure a GRE tunnel between both ABR and advertise on BGP under the are 0 on both routers.