The TTL of a packet is decremented as the packet is processed by the IP process upon reception in the router. The packet gets fragmented, if necessary to traverse the exit network (assuming the packet is not marked DF), by the IP process at the exit interface of the router. The TTL of the resulting packet fragments will be the same as if the packet were not fragmented.
RFC 791, Internet Protocol has a full description of fragmentation, and it explains that the header fields are copied from the original packet to the packet fragments:
To fragment a long internet datagram, an internet protocol module (for
example, in a gateway), creates two new internet datagrams and
copies the contents of the internet header fields from the long datagram into both new internet headers. The data of the long
datagram is divided into two portions on a 8 octet (64 bit) boundary
(the second portion might not be an integral multiple of 8 octets, but
the first must be). Call the number of 8 octet blocks in the first
portion NFB (for Number of Fragment Blocks). The first portion of the
data is placed in the first new internet datagram, and the total
length field is set to the length of the first datagram. The
more-fragments flag is set to one. The second portion of the data is
placed in the second new internet datagram, and the total length field
is set to the length of the second datagram. The more-fragments flag
carries the same value as the long datagram. The fragment offset field
of the second new internet datagram is set to the value of that field
in the long datagram plus NFB.
This procedure can be generalized for an n-way split, rather than the
two-way split described.