There is a vague part about what is "fast" based on what, but with regard to the iPhone, "whether there is a faster charging method than the attached charging adapter" is meaningful. In this regard, the iPhone 6 and newer models launched in 2014 offer a faster way to charge.
The maximum output of the charging adapter (AC-USB adapter) that comes with most iPhones is 5V x 1A = 5W. However, since the iPhone 6 supports a maximum input of 1.4A, it can be charged at 5V x 1.4A = 7W by using a separately sold charging adapter with a larger output. Since iPhone 6 Plus supports input at maximum 2.0A, it can be charged faster with 5V x 2.0A = 10W.
The iPhone 8/8 Plus or later supports "USB PD", so the conditions are even more advantageous. A charging adapter with a USB PD compatible Type-C port and a USB-C to Lightning cable (a cable with a Type-C terminal and Lightning terminal) are required, but a maximum of 18 W and faster charging is possible. Will be.
This means you need a charging adapter (or mobile battery) with a higher power USB port to charge faster. 5V is constant according to the USB standard, so prepare an amperage of 2.0A or more, preferably 2.4A or more. You'll also need a Lightning cable with a high amperage, but it's fine if the product has the MFi (Made for iPhone) logo.
If you aim for a higher charging speed, unify the charging adapter/mobile battery and cable with USB PD. With iPhone X/8/8 Plus or later models released in 2017, you can get the fastest charging environment at present. Note that the iPhone 11 Pro/Pro Max comes standard with this fastest charging environment, so there is no "faster" charging environment.