My recording setup for using an external mic plugged into an iPhone for video:

1) Zoom H4n Pro or summat (https://zoomcorp.com/en/us/handheld-recorders/) (what I use for my audio these days)

2) Long cable headphone jack male (plugged into Zoom H4n headphone jack) to female; for length so I don’t have to put the camera near the recorder if I don’t want to; I usually put the mic up high and behind me or off to my drone side so I don’t end up with chanter heavy recordings.

3) a Rode TRS male (plugged into the cable above) to TRRS male adapter, SC7 I think, the red one (http://www.rode.com/accessories/sc7) – this is required because Apple is TRRS (tip ring ring sleeve), not the usual TRS (tip ring sleeve = normal stereo)

4) Apple TRRS (plugged into the Rode) to lightning adapter into my iPhone using just the video mode in the camera app (https://www.apple.com/shop/product/MMX62AM/A/lightning-to-35-mm-headphone-jack-adapter)

Looks like the H1n at $120 would be a good option for excellent audio without the H4n price.

Outside of Zoom products, if you’re looking for something even cheaper, just make sure to look at its specs and that it can handle 110-ish decibels at a minimum and you should be good.