I swear by my mom I didn't do that.

[tufguy]

1) I swear by my mom I didn't do that.

2) I swear on my mother I didn't do that.

3) I swear on my job I didn't do that.

Please check my sentences.

 

[emsr2d2]

1) I swear by my mom I didn't do that. :cross:

2) I swear on my mother's life I didn't do that.

3) I swear on my job I didn't do that. :cross:

Please check my sentences.

We don't use 1 or 3. If your mother is alive, you can swear on her life. If she's dead, you can swear on her grave.

 

[tufguy]

We don't use 1 or 3. If your mother is alive, you can swear on her life. If she's dead, you can swear on her grave.

I am confused "Where to use 'by' and where to use 'on'?".

 

[GoesStation]

You swear by something that you've found to be reliable: I swear by Vaseline for eczema. You swear on​ something that you value, like your mother's life.

 

[emsr2d2]

The only similar example I can think of that uses "by" is the oath spoken by a witness, for example, in a legal case. "I swear by Almighty God that the evidence I shall give be the truth, the whole truth and nothing but the truth".
("Almighty God" can be replaced by the name of another deity or a holy scripture, depending on the religious persuasion of the person speaking.)

You can read more here.

 

[GoesStation]

American witnesses in court just swear by answering "I do" when asked Do you swear to tell the truth, the whole truth, and nothing but the truth?