Please help me identify this Omega watch

Very sorry if this is in the wrong forum, I wasn't sure where to place it.

So about 7-8 years ago my dad gave me this Omega watch, I've kept it in a draw ever since as to not ruin it from wear and tear and only recently dug it out, because I thought what's the point in being given a watch to put it away to never be touched.

I want to get it serviced as the watch seems to stop intermittently even when I wind it up like 40 or so twists. It wakes up after a couple of shakes and the longest its run for is probably 8 hours before it it stops intermittently again, so something is a bit iffy.

I have asked my dad about the case it came in but he has said he isn't sure where it is and it been a long time since he placed it somewhere. From my research from just looking at the watch and some online sleuthing, it is a Coaxial escapement skeleton watch, one crown and two buttons on each side that adjust date and day of the week, also it seems to be a limited edition as the is a 078/999 etched on the underside suggesting it number amongst 999.

I have tried to look for a serial number even going in with a magnifier and flashlight but can't seem to find one. I have scrolled and traulled through the official Omega website, Google images and other website but cannot for the life of me find this watch.

The watch seems very legit, as the strap, crown, logos all seem to bare the omega brand, but since I am unable to find the watch anywhere I have a sinking feeling it could be a watch made to look like Omega. I have also asked my dad where he bought it from and he said it was from a person from a bidding site similar to Ebay, but was so long ago that he has lost contact.

I want to take it to a Omega service center, and buy a new official strap for it as the current one has stains and crack, but I want to figure out what type of Omega it is first and figure out if i should shell out money to for its up keep.

Here are some photos to accompany what I am saying.

just in case anything is "accidentally" deleted

Thank you, I thought it might be a fake, I knew something was wrong when I could not find anything about the watch and there were a few flags that were suspicious. Thank you and i really appreciate you guys for confirming.

While obviously disappointing, the watch still holds sentimental value, so still precious to me. But thank you guys for the help and its greatly appreciated . 😀

Having taken this watch out and doing research on Omega and stuff it really has given me an interest in watches and if anything has really sparked my interest in Omega watches to the point I really do want to put down some serious money on having my very own Omega.