Formal:
* Intentionally
* Purposefully
* Consciously
* On purpose
* Designedly
* Calculatedly
* Premeditatedly
Informal:
* On purpose
* Knowingly
* By design
* With intent
Other options:
* Willfully (emphasizes a strong desire to do something)
* Calculatedly (emphasizes careful planning)
* Thoughtfully (emphasizes consideration)
The best synonym to use will depend on the specific context and the meaning you want to convey.