Don't worry you will get them if you own private key for that wallet.
That is correct, however, to "cash out" the bitcoin gold without compromising your paper wallet you'll have to jump trough several hoops.
If you ever decide to "cash out" the bitcoin gold, it might be a good idear to sweep the paper wallet into a different bitcoin wallet, wait untill the sweeping transaction has confirmed, and afterwards (and only afterwards) import the private key from your paper wallet into a bitcoin gold compatible wallet.
As soon as your private key is entered in either wallet, your paper wallet must be marked as compromised. As soon as the bitcoin and bitcoin gold are spent, discard and never re-use the paper wallet again... Instead, making a new paper wallet to transfer your BTC to might be a good idear.
Please look up all the forks of bitcoin and when they occurred before discarding any paper wallet! You my be very surprised to find you are entitled to about 8 to 10 different forked coins! Here is what i found.
Bitcoin Cash: Forked at Block 478558[4], 1 August 2017, For each 1 BTC you get 1 BCH
Bytether: Cross fork from Bitcoin to Ethereum blockchain at block 478558, 1 August 2017. For each 1 BTC you get 1 BTH ERC-20 token.
Bitcoin Clashic: Forked at Block 478558[5], 1 August 2017. For each 1 BTC you get 1 BCHC / BCL
Bitcoin Gold: Forked at Block 491407[6], 24 October 2017, For each 1 BTC you get 1 BTG
UnitedBitcoin: Forked at Block 498777[7], 12 December 2017, For each 1 BTC you get 1 UB.
Bitcoin Diamond: Forked at Block 495866[8], 24 November 2017, For each 1 BTC you get 10 BCD
Bitcoin Hot: Forked at Block 498848[9], 12 December 2017, For each 1 BTC you get 100 BTH
Super Bitcoin: Forked at Block 498888, 12 December 2017, For each 1 BTC you get 1 SBTC
BitcoinX: Forked at Block 498888[10], 12 December 2017, For each 1 BTC you get 10,000 BCX
Oil Bitcoin: Forked at Block 498888, 12 December 2017, For each 1 BTC you get 1 OBTC
Bitcoin World: Forked at Block 499777, 17 December 2017, For each 1 BTC you get 10000 BTW
Lightning Bitcoin: Forked at Block 499999, 19 December 2017, For each 1 BTC you get 1 LBTC
Bitcoin Stake: Forked at Block 499999, 19 December 2017, For each 1 BTC, you get 100 BTCS
Bitcoin Faith: Forked at Block 500000, 19 December 2017, For each 1 BTC you get 1 BTF
Bitcoin Top: Forked at Block 501118, 26 December 2017, For each 1 BTC you get 1 BTT
Bitcoin God: Forked at Block 501225, forked on 27th December 2017. For each 1 BTC you get 1 GOD
Bitcoin FILE: Forked at Block 501225, forked on 27th December 2017. For each 1 BTC you get 1000 BIFI
Bitcoin SegWit2X X11 Not to be confused with a previous fork SegWit2X with the same name. Forked at Block 501451, 28 December 2017. For each 1 BTC you get 1 B2X
Bitcoin Uranium: Forking on 31st December 2017, For each 1 BTC you get 1 BUM.
Bitcoin Pizza: Forking at Block 501888, 1st January 2018, For each 1 BTC you get 1 BPA
Bitcoin All: Forking on 1st January 2018, For each 1 BTC you get 1 BTA. Referenced on steemit post.
Bitcoin Cash Plus: Forking at Block 501407, Expected on 2nd of January 2018, For each 1 BTC you get 1 BCP
Bitcoin Smart: Forking at Block 505050, 21 January 2018, For each 1 BTC you get 100 BCS
Bitcoin Interest: Forking at Block 505083, 22 January 2018, For each 1 BTC you get 1 BCI
Quantum Bitcoin: Forking on 28th January 2018, For each 1 BTC you get 1 QBTC
Bitcoin LITE: Forking on 30th January 2018, For each 1 BTC you get 1 BTCL
Bitcoin Ore: Forking on 31st January 2018, For each 1 BTC you get 1 BCO
Bitcoin Private: Forking TBA in January 2018, For each 1 BTC you get 1 BTCP (also if you have 1 ZCL you get 1 BTCP)
Bitcoin ATOM: Forking TBA in January 2018, For each 1 BTC you get 1 BCA
Proposed (but cancelled) coin splits[edit]
SegWit2x: This was a planned coin split of the digital currency Bitcoin, which was later canceled before the split could take place.