Yes, this can be achieved. Whether you have a leased line or if you have both connections in the same geographical area, the configuration is possible. This is a situation where you require a dual homed setup with multiple local routers where these local routers are not necessarily physically local, but can be connected via the leased line. Such a setup can be seen here.
Just keep in mind that your leased line should be able to carry all of the traffic of both sites in case one of the two links goes down. It is also possible to do load balancing in such a case, as is described in the link I shared.
If you have a /24 public IP address space, then you may have a public ASN. That is, an ASN that can be announced by you and your ISP to the global Internet. Your ISP may make your address space part of a larger ASN (that belongs to the ISP) that includes other IPs that are administered by the ISP as well.
If you want an ASN all your own, then you must obtain it (lease it) from one of the Regional Internet Registries, just like blocks of IP addresses. Because these are limited in number, the RIRs are very selective about to whom they grant an ASN.
Alternatively, you can set up your network topology to function with iBGP and have a private ASN. This is not announced to the internet, but can be used by your ISP to properly route data through the appropriate ISP connection to your network.