Adjust the vertical alignment of type on a path

Select the type object.
Choose Type > Type On A Path > Type On A Path Options.
Choose an option from the Align To Path menu to specify how to align all characters to the path, relative to a font’s total height:
Ascender

Aligns along the font’s top edge.
Descender

Aligns along the font’s bottom edge.
Center

Aligns along the point halfway between the font’s ascender and descender.
Baseline

Aligns along the baseline. This is the default setting.
Note: Characters without ascenders or descenders (such as a letter e) or a baseline (such as an apostrophe) are vertically aligned with characters that have ascenders, descenders, and baselines. These font dimensions are permanently specified by the font designer.

For more control over vertical alignment, use the Baseline Shift option in the Character panel. For example, type a negative value in the Baseline Shift box to lower the type.