Who funds it is who owns it
The name on the deed is not what decides the tax. Where co-owners have definite and ascertainable shares, each is taxed on their own share of the rent and gain under Section 26, not jointly, and the share the tax law recognises is the one you actually funded. So if a resident parent is added as a joint name for convenience but the NRI paid the whole price, the property and its future gain are the NRI's; if funding was split half and half, so is the tax.
This matters because adding a name without a matching contribution creates problems: it can be treated as a benami arrangement, or trigger clubbing where funds were given to a spouse, so the income comes back to the real funder anyway. The clean approach is to make the ownership shares on the deed match who actually paid, and keep the bank trail to prove it. That single step prevents most joint-ownership disputes with the tax office.
What you can repatriate depends on the funding
When you later sell your share, how much of the money you can send abroad turns on how you funded the purchase, and there are two distinct limits people often confuse.
If you bought your share with repatriable funds, money from your NRE or FCNR account or a fresh inward remittance, the sale proceeds of your share can be repatriated, but the repatriation of proceeds from residential property is restricted to not more than two such properties. If instead you funded it from your NRO account or with rupee funds already in India, the proceeds are non-repatriable in that sense and go out through the NRO route, which is capped at USD 1 million per financial year across all your NRO remittances. These are two separate rules, the two-property cap under the property regulations and the USD 1 million yearly cap under the remittance-of-assets regulations, so the answer depends on which applies to your share.
The TDS when you eventually sell
The withholding on a later sale also splits by co-owner, because it depends on each seller's residency. On your share as an NRI, the buyer deducts under Section 195, needing a TAN and filing Form 27Q, with no ₹50 lakh threshold. On the resident co-owner's share, the buyer deducts 1% under Section 194-IA with a Form 26QB and no TAN, only if that share is ₹50 lakh or more.
So a jointly owned flat sold later has two deductions running side by side, and treating it as one 1% deduction on the whole, as buyers often do, under-deducts on the NRI's share and exposes the buyer. On your share, the Section 195 deduction is on the gross, so it usually over-deducts against your real 12.5% long-term gain, which you reclaim on your return or reduce up front with a lower-deduction certificate, Form 13, now Form 128. A practising CA sets the funding and shares up cleanly at purchase and handles the split correctly at sale.