i used arduino to control one toy motor with L298N, the motor only want 3-5V voltage . I just have a AC/DC adaptor which can output 9v 1A ,So i used it to supply the arduino and L298N. because the motor is small ,i used a 78L05 to get 5v for L298n Pin4 and connect the adaptor output directly to arduino external powerin . but the arduino seem not to work and blink and the outpin (should high) have no result. After five or later minutes, it work and not blink. i think maybe the adaptor not provide enough current for arduino,but the adaptor output is 1A and 9v , is not enough to driver a small motor and arduino??
Check the specs on your motor. Those cheap low voltage motors take 2 amps easily. Your 1A power supply doesn't come close.
Also, 298N has a minimum motor voltage of 5V (and up to 46V). It doesn't play well with low voltage motors.