My employer doesn't acknowledge my hospital sheet

So, you were given 3 copies of the document showing that your father is sick and unable to work having been hospitalized and now in rehabilitation. Did you send a copy to the employer? If not you need to send them a copy! Otherwise they have no documentation. Maybe it is good to either take a copy there yourself or send one by registered mail (Einschriebung).

But there are laws concerning disability, they cannot just decide not to pay. I am setting 2 links about such things since I am no expert. From, my understanding  an employer needs to pay the normal salary for up to a maximum of 6 weeks. This is known as Entgeltfortzahlung.  An exception is if  they are a civil servant, soldier or judge, then it continues longer.

Then after the 6 weeks, it is the health insurance and not the employer that pays between 70% of the after tax pay and 90% of the before tax pay. This is known as Krankengeld. One can get this for up to 78 weeks in a 3 year period. But there are many details I cannot go into here, best to look at the links provided

https://www.arbeitsrechte.de/entgeltfortzahlung/https://www.arbeitsrechte.de/krankengeld/

You (or rather your father) are required to send the medical certificate, saying that he is unfit for work from XXX til YYY, latest on the third day of being sick (if the employment contract doesn‘t specify a perion shorter than 3 days, which is possible) to the employer.
If you didn‘t, they do not need to continue paying his salary. Submit is now, as soon as possible, and they have to pay again from the day you submit until the certificate expires. If he is sick longer, make sure you submit a new one before expiry!