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I am using Python package lightkurve for exoplanets searching by the transit method. When I download light curve of some star and apply periodogram, I find frequency and power of periodic components in the light curve. However, I noticed that multiples (0.5x, 2x, ...) of the original period are displayed too. Here is example for Kepler-6b.

import lightkurve as lk
import numpy as np

light_curve = lk.search_lightcurvefile("Kepler-6", quarter=1).download().PDCSAP_FLUX
light_curve.scatter()

periodogram = light_curve.to_periodogram(method="bls", period=np.arange(0.5, 10, 0.0001))
periodogram.plot()

I could take only strongest period (3.24 d), but what if there are more exoplanets (1.08 d, 9.71 d, ...)? I thought that if I use the light_curve.fold(period) method, I can tell if it is a transit (there is only drop of flux) or not (there are more drops of flux). However, Kepler-20f has also multiple drops of flux after fold light curve (because of other planets?).

enter image description here

How can I tell if it is a planet transit or not?

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Of course you will get multiple peaks in the periodogram. The Fourier series representing a non-sinusoidal signal will contain frequencies at multiples of the fundamental frequency. Similarly, you can have a periodic signal with double or treble the period which will look identical, but where the phenomenon causing the signal repeats either two or three times during each cycle.

The solution is of course to plot the data folded on the proposed period, as you have done.

In the examples you have shown, clearly the period of 3.23d is the only valid period for a claimed exoplanet, since the transit only takes place once per cycle and there is no sign of any other features or excessive scatter in the folded light curve at that period.

For the 9.71d period to be valid you would either (i) have to have three planets, equi-spaced around the same orbital circle, each with a 9.71d period, and of identical size so that the transits are the same depth. That is not a stable situation. Or (ii) you are unfortunate enough to have one planet with a 3.23d period and another with a 9.71d period that transit at exactly the same time. But it is not possible to do that without having unequal transit depths and causing scatter in the transit shape when folded at 3.23d.

I cannot make out what your point is about Kepler 20f. This would produce a single feature in a light curve folded on a period of 19.48d, but the amplitude of that signal is small (and I can't see it). Both Kepler 20c and 20d produce transits that will be $\sim 10$ times as deep, with periods of 10.8d and 77d respectively.

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