The radius of the orbit of a charged particle in a uniform magnetic field depends on the mass and velocity of the particle. A positron with a lower velocity would have a smaller turning radius than an electron. Could it be that simple?

It´s so simple. Here is the formula for the radius r and magnetic field B, and you see the radius increases with increasing momentum or energy.

r = p/qB

Are you referring to the classic illustration of the discovery of the positron from Anderson's bubble chamber work (Phys Rev 43(491), 1933, Fig. 1)? This shows a positron loosing energy as it passes through a lead plate and thereafter having a smaller radius.

hi  Professor Julyan and professor Bussel  and my best friend mr Krieger thank you answer this question.

 the pair of electron-positron have been produced in the pair production process and we know that these particles acquire equal energy in this process(1.022 Mev)  on the other hand we know electron and positron have equal mass and spin(1/2).my problem is charge of these particles and how these charge cause different spiral in the bubble chamber?(note we assume the magnetic field is equal.)

They are identical, the direction is mirrored.