Destination lat/long based on Distance from origin


I am new to OSM and hoping you guys can provide some guidance on our requirement.

We need to display stationary objects on the map based on “X” distance from an Origin site. Additional requirement is that the final destination point has to be on the road and the distance is traced around the road (i.e. not straight line/great circle).

So far, from what I can gather, if we have the origin and destination lat/long, we can use the standard API to determine distance between the origin and the destination. In our case, however, we have the origin and the distance and need to find the destination point on the street. We can get basic direction of travel from user input (east/west/north/south) but the challenge is that the street curves and we are not sure how to keep the point on the road.

Lastly, our distances are usually between 500-1500 feet…so we are not looking for huge distances.

Any guidance to implement this solution would be highly appreciated.

Can you explain what “distance” means here? It seems you want to display objects which can be reached walking or with a certain vehicle?
So “distance” would be the length of the shortest possible/allowed way? What API do you mean?
You write “the road” or “the street”, so it seems you already know the route that leads to the target?
Or do you mean something like “Isochronen” offered here ?

This project is related to the construction industry and we would like to place construction related signs on the side of the road. These signs have to be a certain distance from each other. Shortest possible/allowed way will work.
Regarding API, previously we were using Google distance API and will be switching to OSM.