on/off filter and their photometric calibration I am reading a paper here

What is off band filter for? If we have already known the positions of the sources we are interested in, then off band filter is useless, correct? So an off band filter is to discovery sources?
An off band filter is usually self-designed? There is no unified standard(central wavelength, band width, etc. )?
For the photometric calibration, when is continuum needed? Since there are standard stars, why is continuum needed?

Thank you. My questions are long, so I put them here.
We assume the continuum is flat, right? The off-band filter is for 1) photometric calibration, 2) discovering new sources?
How to do the photometry then? When do we use continuum and when do we use a standard star?
The on- vs. off-band filter is to let you easily measure the strength of an absorption or emission line in the object's spectrum.   &quot;Off-band&quot; doesn't refer to a shift in position, but rather in the wavelength that the filter lets through. It is &quot;off&quot; the wavelength of a particular spectral line.
This illustrates the idea:

(from Michael Richmond's page here, used under CC-BY-NC-SA 2.0 license).
In this case, the light through the filter shown in red would be affected by the H$\alpha$ absorption line in the star's spectrum, while the light through the filter shown in green would not.  So the ratio of the two would give you a very good measurement of how strong the line is, without worrying about how bright the star is overall, i.e. what the overall continuum level is.
In the paper you're reading, they would be looking for emission lines from planetary nebulae, but the idea is the same - the on-band filter measures line+continuum, and the off-band filter only measures continuum, so it lets you correct for the continuum emission and measure only the line strength.
The design of the filters would depend on which lines you're looking for. In this case they are targeting the [O III] line which is normally at a wavelength of 5007 Angstroms, but because they are looking at distant objects, the emission is red-shifted by the expansion of the universe, so they use a custom filter whose wavelength is shifted to match the red-shifted wavelength of that emission line for this particular group of galaxies.