bootstrap 4 making dropdown scrollable

just you can use @media in your css

@media (max-width: 500px) {
    .dropdown-menu{
        height:200px;
        overflow-y:auto;
    }
}

What I can suggest is in place of hard coding height in pixels you can take the advantage of the view port height like adding this style to your dropdown-menu item or add at the class level

Inline

style="overflow-y:auto; max-height:80vh"

For every dropdown

.dropdown-menu {
 overflow-y:auto; 
 max-height:80vh
}

Use max-height instead of height:

.dropdown-menu {         
  max-height: 200px;
  overflow-y: auto;
}