Update:

The problem is solved. Here is a efficient code which functions.

directory=/users/philipp/desktop/fmri/dataset/subjects
for subject in subj1_exp1
do
for fMRIruns (fitts.Subject_1+tlrc)
do
for TimeWindows ('[21..75]' '[199..253]' '[427..481]' '[489..543]' '[549..603]' '[659..713]' '[837..891]' '[893..947]' '[955..1009]' '[1013..1067]')
do
cd $directory/$subject/Preprocessing
echo "Processing $subject ... $TimeWindows ..."
3dTcat \
-prefix $TimeWindows.$fMRIruns \
-session $directory/$subject/TimeWindows \
-verb \
-tr 1.0 \
$fMRIruns.BRIK\'$TimeWindows\'
done
done
done

Explanation of the code (written in Zsh): This code takes the file "fitts.Subject_1+tlrc" as input. It then creates distinct time windows for all assigned windows in the "for TimeWindows" loop. That is, the here assigned sub-bricks are extracted from the run and copied into distinct time windows as output files. Hope this helps people in the same situation.

Feel free to comment and have a good day. Special thanks to Yasir (the problem solver) if you read this.

Philipp