Having any felony conviction on your record can hinder your ability to get hired for a job. Many employers in different sectors require background checks for new employees. While federal and Connecticut state laws prohibit employers from excluding you as an employee just because you have a felony conviction, the laws do allow employers to deny you employment if the conviction is related or impacts the job for which you applied. In most cases, your felony conviction will impact the job and therefore exclude you from employment. This does not mean you cannot get a job.
However, with a felony drug charge, you may find it is a bit tougher to find someone who will hire you. From the employer's viewpoint, according to Jobs for Felons, the thought is that anyone with a drug charge has a substance abuse history. This makes you seem unreliable and a risk to the employer.
You have to overcome this objection and way of thinking. However, assuring your employer you do not have a drug problem will not likely work. Instead, you need to find industries where employers are willing to give you a chance.
Typically, with a felony drug conviction, you are looking at industries where you need a specific skill or trade. You are not going to have an easy time getting an office job. You may have to do contract work for a while. This means working as an independent contractor.
Once you can show you are reliable and do good work, you may find it easier to get hired by an employer. This information is for education. It is not legal advice.