To add an overflow menu to TopAppBar in Jetpack Compose, use DropdownMenu composable.

First add a state for menu.

var expanded by remember { mutableStateOf(false) }

Then, put a button and DropdownMenu in actions in TopAppBar .

TopAppBar(
  title = { Text("Title") },
  actions = {
    IconButton(onClick = { expanded = !expanded }) {
      Icon(
        imageVector = Icons.Default.MoreVert,
        contentDescription = "More",
      )
      DropdownMenu(expanded = expanded, onDismissRequest = { expanded = false }) {
        DropdownMenuItem(text = { Text("Item1") }, onClick = {
          expanded = false
        })
        DropdownMenuItem(text = { Text("Item2") }, onClick = {
          expanded = false
        })
      }
    }
  }
)

The preview will look like this: