"in the correct way" is correct and usable in written English. You can use it to refer to the proper, accurate, or accepted manner of doing something. For example, "I need to make sure I do my job in the correct way.".
It's taken in the correct way.
I think it's because I'm now using the correct muscles in the correct way".
The arts are a good thing if they dissent in the correct way.
Addressing someone in the correct way can be crucial for making a good first impression.
Only then can his pledge to "sort this in the correct way" be judged.
"We just have to make sure it is inserted in the correct way".
I am confident because I know we work and play in the correct way.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK