Yes, of course there are plenty of jobs that are available for Digital Marketing as a part-time job. What you need to do is to contact small businesses around your locality or in other cities. And if that is out of option and you want to work from home or you want other opportunities, then I would suggest you sign up in major job portals, like LinkedIn, Shine, Monster, Naukri, and some freelancing websites like Upwork, Freelancer, etc. You will receive new offers on these websites, and you could then choose, and select one based on your preferences. You would get all sorts of jobs like Digital Marketing Consultant, SEO Specialist, PPC Analyst, Content Writer, etc.
If you wish to master these skills to advance in the Digital Marketing career, then I would recommend you to check out the Digital Marketing certification course from Intellipaat. As they offer one of the best courses that are aligned with the industry standards. And as a starter, I would suggest you watch our YouTube video on Digital Marketing tutorial for beginner from our experts.