Nanosecond interrupt accuracy on a 64MHz microprocessor
Theoretical considerations
For a digitizing system to detect something with a temporal resolution of \$\Delta t\$, it needs to have a sample rate of at least \$\frac2{\Delta t}\$. That's a corollary of Nyquist's sampling theorem.
In your case, this means that whatever pin might cause an interrupt that somehow notes the time the signal edge happened, you'd need some sampling clock (or, more precisely related to your application: a counter that can be latched on the external signal) running at least at 666.67 MHz.
practical considerations
Nothing short of that will do, unless you can build an external system that somehow converts the event into something slower that can then be observed afterwards to calculate the time it happened.
So, what I'd propose is actually the approach you've been recommended in the comments, namely, using high-speed counter e.g. inside an FPGA to capture the time and read it whenever you're ready with your MCU.
Or, you use the impulse and very fast analog electronics to e.g. kick of e.g. an exponential voltage decay which you can periodically observe and extrapolate from the observed rate of decay the point in time when it got started. That way, you'd actually be trading ADC resolution (interrupt pin: &quot;1 bit ADC&quot;, if you want so) for timing resolution. You'd still need a pretty good ADC and accompanying CPU speed.
In the end, your problem is a hard one, as detecting nanosecond precision pulses is a hard problem – even starting from a PCB layout point of view (the quality of your pulse edge is a function of the signal bandwidth you can transport on your PCB trace – and for a signal with 1/(1ns) = 1 GHz fundamental frequency, this already becomes non-trivial).
You'll probably either need a very fast FPGA, or aforementioned analog time-to-function converter, a moderately fast ADC and a moderately fast FPGA to deal with the ADC data.
scratch that.
I just read up on time-to-digital converters. Maxim (e.g. MAX35102) and TI offer such (other company certainly, too).
As far as I read this, there's different approaches, but the TI TDC7200, for example, uses an internal ring oscillator (which runs at pretty high speeds, giving you high resolution) to run a counter.
The ring oscillator is disciplined against an external clock, so you'll have to make sure your accuracy needs are met by the quality of that clock.