The use of a (quasi)uniform magnetic field opens new possibilities for a production of twisted particles having orbital angular momenta. Quantum states suitable for a production of charged particles in a uniform magnetic field are determined. The particle penetration from a solenoid to vacuum or another solenoid is analyzed in detail. Experiments allowing one successful discoveries of twisted positrons and positroniums are developed. We find a new effect of increasing a uncertainty of phase of the particle rotation with the distance passed by the particle in the solenoid. This effect leads to exciting new possibilities of production of twisted particles in real solenoids without additional devices like particle sources.