Get the position on a circle for the direction you're aiming in Unity

AimingCircle.cs

Vector2 mousePos = _camera.ScreenToWorldPoint(Input.mousePosition);
Vector2 aimDirection = mousePos - (Vector2)_transform.position;
float aimAngle = Vector2.Angle(_transform.up, aimDirection);
if (Vector3.Cross(_transform.up, aimDirection).z > 0)
{
    aimAngle = 360 - aimAngle;
}

Vector3 newPos = new Vector3(_transform.position.x + bulletSpawnRadius * Mathf.Sin(aimAngle * Mathf.Deg2Rad), 
                             _transform.position.y + bulletSpawnRadius * Mathf.Cos(aimAngle * Mathf.Deg2Rad), 
                             0);