How can I get a point position in circle line

Positions on the three-dimensional plane are 45 degrees apart on the circle. The positions corresponding to the angles are indicated on the left. What happens to the position of a random angle coming from the central point of the circle in the 3-dimensional plane on the corresponding circle line? As an example, I try to find the position between two specific positions of a random angle that emerges from the 45 degree circular section of the circle I have specified in blue.

it looks like your circle is horizontal.
in that case,

x = cos(theta) * radius + center.x
y = center.y
z = sin(theta) * radius + center.z

you might swap x and z if it fits your coordinates better

method with center point, radius and angle

        Vector3 pos = new Vector3();

        pos.x = center.position.x + (dist * Mathf.Cos(angle / (180f / Mathf.PI)));
        pos.y = center.position.y;
        pos.z = center.position.z + (dist * Mathf.Sin(angle / (180f / Mathf.PI)));