On Pentium II there is the sysenter instruction. Also AMD has a syscall instruction.

В какой модели AMD появилась инструкция syscall?
В какой модели (архитектуре?) Intel эта же инструкция была скопирована?

Интересуют названия первых моделей и даты (yyyy-MM-dd) их релиза.

https://en.wikipedia.org/wiki/64-bit_computing

1999
Intel releases the instruction set for the IA-64 architecture. AMD publicly discloses its set of 64-bit extensions to IA-32, called x86-64 (later branded AMD64).
2003
AMD introduces its Opteron and Athlon 64 processor lines, based on its AMD64 architecture which is the first x86-based 64-bit processor architecture.
Intel maintains that its Itanium chips would remain its only 64-bit processors.
2004
Intel, reacting to the market success of AMD, admits it has been developing a clone of the AMD64 extensions named IA-32e (later renamed EM64T, then yet again renamed to Intel 64).
Intel ships updated versions of its Xeon and Pentium 4 processor families supporting the new 64-bit instruction set.

Появилась ли она в Pentium IV в 2004-м году?

http://fliplinux.com/64-x4-3.html

Процессор: 1
vendor_id: GenuineIntel
cpu family: 15
модель: 4
название модели: Intel (R) Pentium (R) 4 CPU 3.00GHz
степпинг: 3
cpu МГц: 2800.000
размер кеша: 2048 КБ
физический идентификатор: 0
братья и сестры: 2
core id: 0
Процессоры: 1
апицид: 1
исходный апицид: 1
fpu: да
fpu_exception: да
Уровень cpuid: 5
wp: да
flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov
pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx lm
constant_tsc pebs bts pni dtes64 monitor ds_cpl est cid cx16 xtpr
bogomips: 6000.41
размер clflush: 64
cache_alignment: 128
размер адресов: 36 бит физических, 48 бит виртуальных

https://en.wikipedia.org/wiki/X86-64#Differences_between_AMD64_and_Intel_64