Yes, you can announce the same prefix in multiple location on the Internet. It is called anycast, and you see examples all the time, e.g. Google's
126.96.36.199 DNS server. Google has the network with that host address in many places around the world, and when you try to connect to that host, BGP routes your traffic to the nearest (from a BGP perspective) location.
The real problem you have is trying to connect between the two locations. You cannot connect from the
/24 network at one site to the same
/24 network at a different site. You could do something like having half the addresses at each location, but you will need to have something like a separate link (real or a tunnel) between the two sites, and one site receiving traffic for the other site needs to forward the traffic over the link to the other site.
You really have not provided enough information in order to give a more specific answer.