Sorry, no quick fixes available. If you are really good at chromatic scales you might find Violinia's method works for clarinet, but you have to be really good at knowing whole tones and semitones for it to work as there is not much correlation between fingerings and intervals on woodwind instruments, especially if there are lots of sharps and flats in the key signature.
Some tips that might help:
For major scales with sharps in the key signature, take the tonic (the key note) you are given eg E for E major and go down a semitone, giving D#. This gives you the last sharp in the key signature. Use a mnemonic (eg Father Charles Goes Down And Ends Battle) to find the sharps, stopping when you get to the one you've just worked out. So E major has F, C, G and D sharps.
For major scales with flats in the key signature, find the position of the tonic (eg Ab for Ab major) in the sequence BEADG. (Think 'bead +g'). Then include all the flats to the left of the tonic, the tonic and the next one to the right. So Ab major has B, E, A and D flats.
For minor scales, first work out the tonic of the relative major by counting up 3 semitones from the tonic. (Eg C minor: add three semitones to C giving Eb). Then work out the key signature as above. The harmonic minor scale obeys the key signature apart from the seventh note, which is raised a semitone. So in C minor, the seventh note is raised from Bb to B natural. The melodic minor scale raises the sixth as well as the seventh on the way up, and obeys the key signature on the way down.
Alternatively, write them out in a table and learn them as you would a multiplication table or French vocab, and get someone to test you until you are perfect.
Once you know the key signatures, you still have to train your fingers to play the scale (as I found out to my cost when I took my Grade 8 recorder in the summer).
What grade are you doing?