This depends on your jurisdiction, and in many places precedence has been set by case law.
But generally, unfortunately, no. If you create something "on the clock" or using your employer's hardware (even in your free time), then the copyright is typically implicitly transferred to your employer.
EDIT: This is actually covered in season 1 of Silicon Valley... Yeah, legit reference, I know ;)
This is true only if explicitly called out in documents you sign when you join the company, or sign a consulting contract. There needs to be language that calls this out.
Mind you, pretty much every US company has that as part of their HR policy or contract agreement.
Other countries don't necessarily have it spelled out so clearly, but instead leave it to case law. However, it's mostly the same around the globe.
The contracts are so your employer owns inventions created outside of work hours, not using employer equipment. This part of your employment agreement is actually frequently contested and deemed unenforceable unless the work is in the same area of expertise as your full-time employment i.e. using knowledge from your job. But it comes down to individual cases.
EDIT: It's covered on the Wikipedia page I've linked. However, just to clarify, the act of being employed is automatically considered work for hire by the legislation. If you're not an employee, but rather a contractor, then you may explicitly form a work for hire agreement in writing as part of the contract.
But generally, unfortunately, no. If you create something "on the clock" or using your employer's hardware (even in your free time), then the copyright is typically implicitly transferred to your employer.
EDIT: This is actually covered in season 1 of Silicon Valley... Yeah, legit reference, I know ;)