in draw event:

if (!variable_local_exists("x1")) {
    x1=room_width/2-100;
    y1=room_height/2;
    x2=room_width/2;
    y2=room_height/2-50;
    x3=room_width/2+100;
    y3=room_height/2;
    click=0;
}

scr_3bezier(x1,y1,x2,y2,x3,y3);

x0=mouse_x;
y0=mouse_y;

if (mouse_check_button_pressed(mb_left)) {
    if (point_distance(x0,y0,x1,y1)<=3) {
        click=1;
    }
    if (point_distance(x0,y0,x2,y2)<=3) {
        click=2;
    }
    if (point_distance(x0,y0,x3,y3)<=3) {
        click=3;
    }
}

if (click=1) { x1=x0; y1=y0; }
if (click=2) { x2=x0; y2=y0; }
if (click=3) { x3=x0; y3=y0; }

if (mouse_check_button_released(mb_left)) { click=0; }
draw_set_color(c_red);
draw_circle(x1,y1,3,0);
draw_circle(x2,y2,3,0);
draw_circle(x3,y3,3,0);
draw_set_color(c_black);

in script scr_3bezier:

var x1,y1,x2,y2,x3,y3,xx,yy,xp,yp,t;
x1=argument0;
y1=argument1;
x2=argument2;
y2=argument3;
x3=argument4;
y3=argument5;

xp=x1;
yp=y1;

for (t=0; t<=1; t+=0.02) {
xx=2*t*(1-t)*x2+power(t,2)*(x1+x3)+x1*(1-2*t);
yy=2*t*(1-t)*y2+power(t,2)*(y1+y3)+y1*(1-2*t);

draw_line(xx,yy,xp,yp);
xp=xx;
yp=yy;
}