Is it permissible for my wife to break her fast in Ramadan due to taking medications that affect her psychological state and prevent her from fasting, knowing that she still has to make up days from last Ramadan?

It is not permissible to delay making up missed fasts until after the next Ramadan unless there is a valid excuse. Similarly, it is not permissible to break the fast in Ramadan except for a legitimate Shar'i (Islamic legal) excuse, such as an illness where fasting would be difficult.

If the described condition has no impact on her health, or if it does have an impact but medication can be taken at night, then it is not permissible for your wife to delay making up the fasts, nor to break the fast in the upcoming Ramadan.

However, if her condition is considered an illness that affects her mental or physical health, as confirmed by a trustworthy doctor, and stopping the medication would worsen the illness or delay its recovery, and it is not possible to take the medication at night, then she may delay making up the fasts and it is permissible for her to break the fast in Ramadan until her excuse is no longer present.

Fasting is considered forbidden if it harms the sick person, and harm is determined by direct experience or by the report of a knowledgeable, trustworthy doctor.