Please use my ltsp.conf file here exactly.

# Don't function as a DNS server: port=0 # Log lots of extra information about DHCP transactions. log-dhcp # Set the root directory for files available via FTP. tftp-root=/tftpboot # The boot filename, Server name, Server Ip Address dhcp-boot=undionly.kpxe,,<fog_server_IP> # Disable re-use of the DHCP servername and filename fields as extra # option space. That's to avoid confusing some old or broken DHCP clients. dhcp-no-override # inspect the vendor class string and match the text to set the tag dhcp-vendorclass=BIOS,PXEClient:Arch:00000 dhcp-vendorclass=UEFI32,PXEClient:Arch:00006 dhcp-vendorclass=UEFI,PXEClient:Arch:00007 dhcp-vendorclass=UEFI64,PXEClient:Arch:00009 # Set the boot file name based on the matching tag from the vendor class (above) dhcp-boot=net:UEFI32,i386-efi/ipxe.efi,,<fog_server_IP> dhcp-boot=net:UEFI,ipxe.efi,,<fog_server_IP> dhcp-boot=net:UEFI64,ipxe.efi,,<fog_server_IP> # PXE menu. The first part is the text displayed to the user. The second is the timeout, in seconds. pxe-prompt="Booting FOG Client", 1 # The known types are x86PC, PC98, IA64_EFI, Alpha, Arc_x86, # Intel_Lean_Client, IA32_EFI, BC_EFI, Xscale_EFI and X86-64_EFI # This option is first and will be the default if there is no input from the user. pxe-service=X86PC, "Boot to FOG", undionly.kpxe pxe-service=X86-64_EFI, "Boot to FOG UEFI", ipxe.efi pxe-service=BC_EFI, "Boot to FOG UEFI PXE-BC", ipxe.efi dhcp-range=<fog_server_ip>,proxy

As long as you have at least dnsmasq 2.76 or newer it will work correctly. Don’t forget to replace <fog_server_ip> with the IP address of your fog server.

ref: https://forums.fogproject.org/topic/8725/compiling-dnsmasq-2-76-if-you-need-uefi-support/5