Student or Learner
I have to send it to my teacher still today.
I have to send it to my teacher today yet.
which sentence is the correct one, please?
Even though language is living, it still has to be comprehensible and logical. Your sentences are ungrammatical in English. Sorry. Even as possible poetry they fail to make sense and sound like a non-English construction.
I'm not a teacher, but I strongly concur with Anglika's summary. One other way to phrase it might be "It's due today, but I have yet to send it to my teacher." As a native speaker, I actually found the contstructions you asked about difficult to say out loud because my natural word order patterns kept imposing themselves when I read the words.