Wayne Michael Wightman, 38, of Carlton Road, Boston, admitted using a car without insurance and also to failing to provide a blood sample for analysis.
Marie Stace, prosecuting, said offices stopped the Citroen DS3 car at 3.35pm on February 13 in Granville Street for a document check and saw the child strapped into the front passenger seat with just a seat belt.
She said it was discovered the car was not insured for Wightman to drive and although he passed a breath test for alcohol, he gave a drugs wipe which showed him to be positive for cocaine and he was arrested and the vehicle seized.
Ms Stace said that at the police station he refused to give a blood sample, saying he was frightened of needles.
Mitigating, Philippa Chatterton said the child had been in a seat belt in the front seat because he was autistic and would unpick any normal set belt and so he was on the front seat so he could be kept keep an eye on.
She said he had been driving his sister's car and thought he was covered by his own insurance, but he wasn't.
She said Wightman had used cocaine for the first time four days before during a rare night out and had not been aware the drug stayed in the system for so long and that the pressure of being in a police station had led to his fear of needles stopping him allowing a sample to be taken.
Wightman was banned from driving for a year but was offered a drivers' rehabilitation course which will reduce the period of the ban by three months.
He was also fined £120 and ordered to pay £119 in court costs and charges.