I am neither a German speaker nor a clarinet player, so please make sure to translate the German text yourself!
This music comes from the Carl Baermann's Vollständige Clarinett Schule (Complete Method for Clarinet), Book 2 (Op. 64). The photo in the question is of the 5th study, Mein Liebster Gedanke (My Dearest Thought).
Op. 64 gives no information as to what any of the symbols mean (which is probably where OP's confusion stemmed from) but it does mention that Op. 63 provides an explanation. The original German text of Op. 63 mentions the following:
Bei den beiden Tönen Fis und Cis ist nebst dem was von F und C gesagt besonders zu bemerken:
a) dass beide Töne auch durch die Aushebung, welche mit dem Daumen der rechten Hand gegriffen wird, genommen werden können, welches in vielen Fällen sehr erleichtert, namentlich in ähnlichen Stellen wie z. B.:
...which translates as:
In addition to what was said about F and C, the two tones F sharp and C sharp should be noted in particular:
a) that both tones can also be taken by the key which is played with the thumb of the right hand, which in many cases makes it much easier, especially in similar passages such as:
This key is not present on modern clarinets.
Op. 63 and Op. 64 are available on IMSLP: