To try to simplify things (even though this may seem extremely complicated), there are at least four types of recorder in modern-day use. I suspect that you have the type that may be called Baroque which has F fingered T123467. Another similar-looking type with simplified fingering is called German which has F fingered T1234. Then there is a type (which looks different from yours) called Ganassi which has F fingered T12346. Finally there are Renaissance recorders (which also look different from yours) which may have a variety of fingerings for F.
An excellent resource resource for recorder fingerings can be found at http://www.recorder-fingerings.com/en/index.php
An excellent resource on all things recorder may be found at http://www.recorderhomepage.net
To answer your question, on a Baroque fingering recorder, T1234 will produce a note that is a microtone between F and F#–in other words, an out of tune F that is on the high side.